The theme of particularly pious or worthy humans becoming angels or at least "angel-like" seems to have been widespread enough already around the 2nd century C.E.. To quote David Hamidovic's book L'insoutenable divinité des anges (translation from French by me):
A similar trend emerged at the same time, in the first centuries of our age
in the context of apocalyptic literature: some human beings can transform into angels, they are "angelified".
He then details the example of Enoch who in several apocryphal texts (both Jewish and Christian) is said to have become the angel Metatron.
A nice overview on several occurrences of this trend is given by Daniel C. Olson in Section III of his article "Those Who Have Not Defiled Themselves with Women": Revelation 14:4 and the Book of Enoch. The end of the section is particularly relevant to this question, and I think it's worth quoting it in its entirety:
The theme of the Christian as angel is not frequent in the literature of
the second century C.E., but it does occur in a wide variety of contexts - a
book of apocryphal acts, a martyrology, an apocalypse, and theological
essays. What is most interesting is that the idea appears only briefly in most
cases and is never elaborated, just as in the New Testament.
In the Acts of Paul and Thecla (late second century C.E.), we read this
beatitude: "Blessed are those who have fear of God, for they shall become
angels of God." The author of the Martyrdom of Polycarp (ca. 155-160
C.E.) remarks almost casually that when certain early martyrs were being
burned alive they apparently evinced no sign of pain, indicating that they
were "no longer men but were already angels" (μηκέτι ἄνθρωποι, ἀλλ' ἤδη ἄγγελοι ἦσαν, Mart. Pol. 2:3). In the Vision of Isaiah (Ascension of Isaiah 6-11), a Christian apocalypse written sometime in the second century (possibly late in the first), we read how Isaiah received a glorious robe and
became "equal to the angels" (Ascension of Isaiah 8:14-15). In the seventh
heaven he also sees Enoch and other ancient worthies "like the angels" (9:8-9). It is not clear whether the author believes humans actually become
angels (in 9:28-29,41-42 he seems to distinguish between the two), but it is
striking nonetheless, that Isaiah is full of curiosity about the heavenly books (9:19-23) and wants to know how and when the righteous receive their crowns and thrones (9:11), and yet seems to take the angelic transformations of 8:14-15 and 9:8-9 as a matter of course. Clement of Alexandria (Frg. 2) alludes to Christians becoming angels, without giving any details. Near the close of the second century, Tertullian (De res. carn. 62) is fastidious enough to devote a short paragraph to the subject, carefully maintaining an ontological contrast between angels and glorified saints, but elsewhere (De orat. 3) he has no inhibitions about calling Christians "candidates for angelhood" (angelorum candidati).
Everything points to a widespread understanding among the earliest
Christians that the redeemed are destined to acquire angelic status and perhaps even become angels, but the concept is apparently so well known and so uncontroversial that neither explanation nor defense is believed necessary.
That it happens is taken for granted, but the questions how it happens, why it happens, or even when it happens (at death? at the general resurrection? upon ascending to heaven?) are barely touched upon.
Just to clarify the above quote, the mention of the New Testament in the first paragraph refers to the following passage in the Synoptic Gospels (here taken from Luke):
But those who are accounted worthy to attain to that age and to the resurrection from the dead neither marry nor are given in marriage, and they cannot die any more, because they are equal to angels (ἰσάγγελοι) and are sons of God, being sons of the resurrection.
Luke 20:34-36
