As mentioned in a comment, ἄνωθεν is an adverb, not a substantive (i.e. noun or adjective). Because we are not dealing with an article-substantive in a modifying relationship, we need not conjecture that ἄνωθεν is itself somehow plural, to agree with the number of the article. This is good since adverbs (as also mentioned) have no number, either semantically or syntactically.
Instead, the article is being as a substantiver. That is, the article has made the phrase τῶν ἄνωθεν into something that can be conceptualized as a "thing" (or "things" in this case). This structure is very common in Greek (though not in English). On this I will quote Dan Wallace, whose work on the article in NT Greek is well respected (bold mine):
The article can turn almost any part of speech into a noun: adverbs, adjectives, prepositional phrases, particles, infinitives, participles, and even finite verbs. As well, the article can turn a phrase into a nominal entity. This incredible flexibility is part of the genius of the Greek article.*
In the case of substavantized adverbial phrases, we often find that in English a noun is required to render an intelligible translation, even the most literal. So in John 8:23:
ὑμεῖς ἐκ τῶν κάτω ἐστέ, ἑγὼ ἐκ τῶν ἄνω εἰμί
You are from the [places] below; I am from the [places] above
This example also uses a plural article, similar to the OP's question. The number simply indicates that the implicit noun idea is plural. This is grammatically different from saying that the adverb itself has number, but the meaning is essentially that of a plural noun whose meaning can be derived from the adverb.
Another example, from Col 3:2:
τὰ ἄνω φρονεῖτε, μὴ τὰ ἐπὶ τῆς γῆς
Think of the [things] above, not the [things] on the earth
Here translations use the more generic noun "things" rather than "places" because further identification is not provided by the context. Similarly we can give a literal translation of John 19:23:
ἐκ τῶν ἄνωθεν ὑφαντὸς δι᾿ ὅλου
from the [things] above, woven through all
A weaver would be better suited that I to further identify "things" in this context, but presumably something like "threads". The warp threads which are held vertically on the loom and extend "through all" the fabric only if there is no seam ("ἄραφος") strike me as the most likely candidate.
*Daniel B. Wallace, Greek Grammar Beyond the Basics: an Exegetical Syntax of the New Testament (Grand Rapids: Zondervan, 1996), p. 231. The examples are also courtesy of Wallace's discussion in the following pages.