A search of the Early English Books Online database turns up multiple instances of "for the tyme being" used in a seemingly modern sense akin to "currently" or "at this time"—and without being embedded in any longer surrounding phrase to clarify its meaning—in records written between 1503 and 1538.
From Richard Arnold, In This Booke Is Conteyned the Names of ye Baylifs Custos Mairs and Sherefs of the Cite of Londo[n] from the Tyme of King Richard the Furst ... (1503[?]):
And yf ony persone or persones at ony tyme after the fyrst daye of this present parlement accepte or Purchace your lettres patent{is} of ony off ye sayde honours Castels Lordships Townes townships Manner Landis tenementis Wastis rentis Reūcions fees feefermes and seruic{is} wt all other appertinaunce or ony dyscharge or quyt clayme as is aboue reherssed or ony of the premisses or ony other possessions of fee or of freholde that shulde growe vnto yow in the tyme comynge bee the wey of forfeytour or other wyse but yf it so •e that this lettres patentis passe be aduyse and assent of your chaunce∣lar and tresorer of England preuyseale and vi. Lordis of youre greate councel for the tyme being and that they and eche of them. Subscribe in suche lettres patentis there names and that theis lettres patentis Soo subscribed wyth the sayd names be Inrolled in youre chauncery of Record.
From The Statutes Prohemium Iohannis Rastell (1527):
The shyryffis of euery counte for the tyme being at the next counte after that the wryt comyth vnto thē for the leuey •xp•sis of the knyghtis shall make opī {pro}clamaciō that the coroners & euery chefe cōstable of the {con}trey of the sayd cofites & the baylyffis of euery hundred or wapentake & all other that will be at the •essing of theyr wagis that he be at the next coūtie to assesse theyr seyd wagis.
...
That eueryone now beīg or here aft be ī the kīg{is} wag{is} of ware beyonde the see or vpō the see haue at his pleasure the {pro}teccyō of {pro}fecture or morature cūclā volumus and in the excepciō of the sayd {pro}teccyon be made comyssyon of assisys and so to be alowed in al the kinges courtes except in accious of det takyn by the kīg or any other to his vse or to the vse of the executours of kīg hēry the .vii. & ī appel{is} of murdre & felony & yf this ordeynaūce be not suffyciēt to ease thē thē the kyng and his councel for the tyme being may graunt {pro}teccyons to euery of them during the tyme thei contynew in the sayd warrys.
From Anthony Fitzherbert, In This Booke Is Contayned the Offices of Sheryffes, Bailliffes of Liberties, Escheatours Co[n]stables and Coroners [and] Sheweth What Euery One of The[m] Maye Do by Vertue of Theyr Offices, Drawen out of Bokes of the Comon Lawe [and] of the Statutes (1538[?]):
Alo it appereth by ye statute made An. 1. H. 4. Ca. 14. yt al appeals to be made of thīg{is} done out of the realme of Englande shalbe tried, and determyned before the Cōstable, & Marshal of Englande for the tyme being
¶ Also when bataille is ioyned in a wryt of right or in Appeale, that shal ••derayned before the Cōstable and Marshal, howebeit the Iustic{is} must ••the bataile done, bycause that they •e properly Iudges therof and not 〈…〉 Constable, nor the Marshal.
And from The Statutes Whiche the Iustices of Peace, Mayres, Shyryffes, Baylyffes, Constables, & Other Officers Were of Late Commaunded by the Kynges Maiestye to Put in Execution, on Peyne of His Graces Moste Hyghe Indignation and Displeasure (1538):
Be it enacted ordeyned and establysshed by the kynge our soueraygne lorde, and the lordes spirituall and temporall, and the cōmons in this present parlyament assembled, and by thauctoritie of the same, that yf any persone or personnes, dwellynge demurrynge inhabytynge or resiant within this realme, or within any other the kynges dominions seignouries or countreys, or the marches of the same, or elles where within or vnder his obeysaunce & power, of what estate dygnitie preeminence order degre or condicion so euer he or they be, after the laste daye of Iulye, whiche shalbe in the yere of oure lorde god. M.D.xxxvi. shall by wrytynge, cyfrynge, printinge, preachinge, or teachyng, dede or acte, obstinatly or maliciously, holde or stande with, to extolle setforth maynteyne or defende the aucthoritie iurisdiction or power of the bysshop of Rome, or of his see, heretofore claymed vsed or vsurped within this realme or in any dominion or countreye beinge of within or vnder the kynges power or obeyssaunce, or by any pretence obstinately or maliciousely inuente anye thynge for thextollynge auauncement settynge forth mayntenaunce or defence of the same, or any part therof, or by any pretence obstinately or malyciousely attribute any maner of iurisdictiō aucthoritie or preheminence to the sayde see of Rome, or to any bysshope of the same see for the tyme being within this realme or in any the kynges dominions or countreys: that thenne euerye suche personne or personnes, so doynge or offendynge, their aydours, assistentes, comforters, abbettours, procurers, maynteyners, fautours, counsaylours, councelours, and euery of them, beynge therof lawfully conuicted, accordinge to the lawes of this realme, for euery such defaulte and offence, shall incurre and runne into the dāgers, penalties, peynes, and forfaytures ordeyned and prouyded by the statute of prouysyon & premunire, made in the .xvi. yere of the reygne of the noble and valiaunt prince kynge Rychard the seconde, agaynst suche as attempt procure or make prouysyō to the see of Rome or els where, for anye thinge or thynges to the derogation or contrary to the prerogatiue royall or iurisdictiō of the crowne and dignitie of this realme.
Evidently, any broader logical context that might explain the logic of the phrase "for the time being" and that may have determined its original formulation was already lost to contemporaneous English, in favor of instant recognition of the set phrase, by no later than the early 1500s—and perhaps much earlier. Certainly, the authors of the documents cited above saw no need to clarify what they meant by "for the tyme being" by linking it to some external anchor such as "for the tyme being present" or "for the tyme being considered" or "for the tyme being in effect."
Christine Ammer, The American Heritage Dictionary of of idioms, second edition (2013) offers this oddly backward catchall entry for "for the moment," "for the present," and "for the time being":
for the moment Also for the present; for the time being. Temporarily, during the period under consideration, for now. [Examples omitted.] The first term dates from the late 1800s, the first variant from the mid-1500s, and the second variant from the late 1400s.
So, according to Ammer, "for the time being" came first (late 1400s), followed by "for the present" (mid-1500s), followed by "for the moment" (late 1800s). How that makes "for the time being" the "second variant" I do not know, but clearly Ammer isn't approaching the notion of variants chronologically.
Other dictionaries of idioms that I consulted—from Oxford, Cambridge, Longman, and Wordsworth—have entries for "for the time being" but offer no insight into how or when the phrase arose.
Update (September 24, 2023): Eearlier EEBO instance of 'for the time being' (differently spelled)
Prompted by a comment from site participant TimR that mentioned the spelling 'beynge' (a spelling that I hadn't used in my previous searches, I revisited Early English Books Online to see if any earlier instance of the expression with that or a similar spelling might appear in the EEBO database. They do. Please note that EEBO cintains books only for the period 1475–1700, and therefore my answer (which purports only to discuss the results of EEBO searches is therefore limited to instances from 1475. With that proviso explicitly stated, I note the following occurrences.
From a 1485–1486 translation of Dominican Laurant, This book was compyled [and] made atte requeste of kyng Phelyp of Fraunce ... whyche book is callyd in frensshe. le liure Royal · that is to say the ryal book. or a book for a kyng:
Fyfthly whan a creature is accustomed to bye rētis or other thynges. by suche condycyon. that yf wyth incerteyn tyme. hys money be not rendred ne payed ageyn / he shal haue that thynge / and for the tyme of the sayd beyng he byeth it for lasse than it is worth· And he seeth clerely that he that hath solde that hath not. ne shal not haue at the terme power to paye ne to rendre that whyche is lente. And yf he haue not the power in thys hope & wylle / he gyueth hym tyme of rechate or byeng ageyn / that thenne he shal haue the prouffyte of the thyng. and with that he shal haue ageyn al that he hath lente wtthoute ony thynge to abate therof.
From Here begynneth certayn statutes and ordenaunces of warre made ordeined enacted and estalysshed [sic] by the most noble victorious and most cristen prince oure moste drad souerayn lorde King Henry the vii. King of Fraunce and of Englond by the aduyce of his noble and discrete counseyl holdynge than his hygh courte of his parlament at his paleis of westmynster the xvii. day of October in the yere of oure lord god M.CCCClxxxxii and of his moste noble reigne the vii. yere (1492[?]):
Firste that almaner of men of the kinges ofte of what nacion. estate or condicion soeuir they be. be obeissaunt vnto the kinge oure souerayn lorde vpon peyne of drawinge hanging & quarteringe And ouir that that euery man aforsaide the kinges lieutenant for the tyme beinge only excepte be obeissaunte vnto the marshal of the hath aggreed with his capitaigne aftre the warde of the courte.
From Anno xi henrici vij Statuta bonu[m] publicum concerne[n]tia edita in parliamento tento apud westmonesterium xiiij die Octobris anno regni illustrissimi Domini nostri regis Henrici septimi (1500):
That vnto the knyghtes & citezins of euery shire and cyte assembled in this present parlyament. barons of the .v. portes & certain burgeyses of Burgh townes or they frō depart this p̄sēt. parlyamēt be deliuered of euery weighe & mesure whiche now our soueraȳe lord hath caused to be made of brasse for ye comȳ weele of all his subgett & lyeges withī this his realme Englōd acordȳg to ye kȳg our souereyne lordis standard of his Echequer of weyght and mesures as they ben in the eschequer of our sayd souerayne lorde and that the sayd knightes Cytezyns and Burgeyses to whom the sayd weyghtes & mesures shull be delyuered as is afore sayd surely conuey or cause ye same to be conueyed on this half the feste of Ester nexte comyng by the sayd Ci¦teyzins to theyr Cytees and by the sayd knyghtes vnto suche Burgh or towne corporate / or market Towne within the shyre for whiche they ben elected as is specifyed & conteined in a sedule vnto this present byll annexid. there to remayne for euer in the kepinge of the Mayre Baylly or other heed Offycer for the tyme beinge of the same Cytee Burgh or towne as the kynges standarde of weyght and mesure / And that thinhabytauntes of all Cytees Burghs and market Townes within eueri of the sayd Shyres.
...
Prouyded also that the examynacyon of defawtes abouesayd and punysshment to the offenders of euery offence commyted hereafter within ony of the sayd .v. portes / shall be had done & admystred by the lorde wardeyn of the sayd .v. portes or by his lyeutenaunt of the same for the tyme beynge & none other the premysses notwithstondynge ...
This book has at least fifteen additional instances of "for the time/tyme beinge/beyng/beynge"—most of them evidently in the sense of "at this time."
It thus appears that, in the era of printed books in English (which began in 1475, according to EEBO), forms of "for the time being," in the modern sense of "currently" or "at this time" appear in texts at least as as early as 1485.