Actually, we do idiomatically say "In an instant" in English. We just do not put "the completion of" in front of it. This measure of time is indivisible and immediate anyway, so that would not make much sense. See the Century Dictionary and Cyclopedia s.v. instant II 2:
A point in duration; a moment; very small period or interval of time: as, he will return in an instant
This gracious all-commanding beautfy fades in an instant. Burton, Anat. of Mel. P. 536
An instant … is that which takes up the time of only one idea in our minds without succession of another, wherein therefore we perceive no succession at all.. Locke, Human Understanding, II, xiv. 10.
Now, perhaps I misunderstood and you only meant that the latter two idioms are not said in English, but you might want to reconsider this form even if you dismissed it. Since it is less direct than instantly, instantaneously or immediately, it does have a slightly fanciful connotation to it.
The term has been with us since at least the 17th century, as demonstrated by An Apologie of the Power and Providence, which was written by George Hake and published in 1635. The phrase is used four times on page 34 and at least twice in this single sentence:
Now as all creation is immediately by the hand of god soe is it undoubtedly in an instant which is one of the special conditions and properties whereby it is distinguished from generation, the latter requiring time for perfecting thereof, at leastwise in regard of the previous disposition thereunto, though the introduction of the forme bee indeed in an instant, but the former requires no time because it works without all motion or preparative alteration.
It also works quite well to describe feats of heroism as demonstrated by these contexts:
In an instant, Robin, in whose generous heart the feeling of hate had no place, bounded to his rescue. He seized the tail of the tiger and struck him a tremendous blow with his stake."
The Crusoes of Guiana: Or, The White Tiger by Louis Boussenard
For a moment the two men looked into each other's eyes, with hatred like a naked sword between them; and then Guy of Gisborne laughed exultantly and cried out: ' You were ever a fine bowman, but I think you have loosed your last arrow—Robin Hood!'
In an instant robin had sprung to his feet and turned to leap down the steps. Behind him he heard a bellow of astonished rage from the sheriff, and the voice of his old enemy shouting to the men-at-arms to shake him.
The Chronicles of Robin Hood by Rosemary Sutcliff
And why would he, when he could simply fumble in his sunflower-yellow utility belt and produce a gadget that would save him in an instant?
News Statesman, Limited, 2005, page 29, in reference to Batman.
Granted, there are more mundane contexts in which this word can be used too, but I suppose you can see how this usage is fitting. It also seems to be as close of a match to the literal translation you gave as possible, which can help avoid adding unintended connotations to the translation.
Compare with in a jiffy which has effectively the same meaning, except usually more informal and perhaps slangy, despite some niche technical uses, lending to the comparative formality of in an instant. Jiffy is more likely to be used by mechanics than in reference to heroes.