Thong has been applied to shoes since the late 1940s and early 1950s, and to skimpy underwear since 1975.
Early History: Thong as Thin Leather Strap
Of course it has been applied to clothing far longer than that. Thongs have been wearable for a very long time. In Middle English, they would have referred to laces, bands, and other thin leather strips. This sample from the Oxford English Dictionary (in "thong, n.") shows thongs being used as a shoelace:
c1200 Trin. Coll. Hom. 137 Ich nam noht ne forðen wurðe þat ich un-cnutte his sho þuong.
(My translation) I am not, nor even worthy enough that I untie his shoe lace (thong).
The Middle English Dictionary construes "thonged shoe" as a laced shoe ("sho, n." 1b). The same dictionary's entry for thong emphasizes its use as a strap, cord, or belt (2). Here is a gloss that equates a thong to a girdle:
c1400 Gloss.Bibbesw.(Hrl 490)190 : Thwange, gyrdyl [glossing AF (Cmb): ceinture].
Lexicons of Early Modern English connects thong to a widening array of clothing. Here is an entry in the 1499 edition of the Promptorium Parvulorum that equates thong and the Latin word for a shoe strap:
Lad or thonge. Ligula ...
Other entries emphasize buckler straps, straps on weapons, yoke fasteners, belts, the bridle throatband, the name of a castle in Lincolnshire, leashes, and the like. It was a golden age for the thong, which seemed to stand for many items of clothing and tools that were made of leather straps.
In A New English Dictionary (1735), thongs were even used to "bind the loins," which is suggestive of how girdles could be thought of more intimately than their function as a belt or fastener would suggest:
GIRDLE, a Band, Ribbon, or Thong to bind about the Loins
Loins could refer to either the hip area or, as the Oxford English Dictionary coyly puts it, "as the part of the body that should be covered by clothing and about which the clothes are bound" and "as the seat of physical strength and of generative power" (2b). So a thong could be a sensuous belt.
Thong as Sandal
The modern application of thong to shoes and underwear themselves occurs in the 20th century. Up to about the mid-1950s, it is common to see references to thongs in clothing ads, though they often refer to the material of construction. Here is one from 1946 that lists a "primitive thong sandal" ("Display Ad 56 -- no Title." The Atlanta Constitution (1946-1984), Apr 03, 1946, pp. 16. ProQuest. All images used under fair use.)
Here is another ad from 1953. Note how thong describes the quality of construction of the sandal pictured - thin leather straps secured to the sole at three points ("Display Ad 197 -- no Title." The Atlanta Journal and the Atlanta Constitution (1950-1968), May 03, 1953, pp. 1. ProQuest):
This is the style that would eventually be identified as a thong in footwear. This usage ("thong sandal") is already emerging in the early 1950s, though it would take time to disseminate. Notice the usage of thong by itself to specify "one pair" ("Accent Sports Costumes with Gay Casual Shoes." The Atlanta Journal and the Atlanta Constitution (1950-1968), Jul 13, 1952, pp. 1. ):
Thonged leather sandals with a mere strip fastening, or perhaps a buckled T-strap version, are the shoes most likely to succeed with denim playclothes. One pair is a bare-back thong with contoured straps of white smooth leather that insure secure fit.
In good journalistic style, the first instance defines the thong alongside its apparatus ("leather sandals"). Then usage takes a turn - a "bare-back thong" defines "one pair." Such substantive usages would become more common in the coming decades.
Thong as Panty
As for underwear, thong-like designs were around at least as far back as the bikini brief. Lessons in Lingerie by Rebecca Aspan (2012) cites the first appearance of the thong as a design at the New York World's Fair in 1939, and the introduction of the thong as a named undergarment to Rudi Gernreich in 1975. Here is a 1975 advertisement ("Display Ad 281 -- no Title." The Atlanta Constitution (1946-1984), Oct 19, 1975, pp. 1. ProQuest.):
"The nylon panty, a smidge of thong" - note the profile shows a relatively thin strip around the waist and in the back. I've searched a number of advertisements; before 1975 thongs refer to sandals and occasionally other straps; at and after 1975 the underwear is quite common. Here's an article from early 1976 (Smith, Sally. "Valentine Suggestions Range from 'Cute' to Ridiculous." The Atlanta Constitution (1946-1984), Feb 12, 1976, pp. 1. ProQuest):
And the saleslady [at Frederick's of Hollywood] said she was trying to track down a few pairs of "candy pants", a thong underwear with a brief that is little more than a G-string:
We have worn thongs ever since.