Speaking in tongues is much older than Paul.
It comes from the Pythoness of the Oracle at Delphi. How it worked was you made a large donation to the Temple of Apollo and you got the ask the Pythoness a single question. She would the pray to the God Apollo at a fissure at the altar. Recently tested it was found that a mildly toxic gas was, and still is, emitted from this crack in the Earth. The Oracle is over the junction of two earthquake faults. She, the Pythoness, would start dancing around and babbling incoherently. A Priest of the temple would "translate" what the Pythoness had said. She was speaking the speech of the gods and was getting all her information from Apollo.
The Oracle at Delphi started in the 400s BC, when Greece was at its strongest. It continued into the Roman era as if it was a parody of its former self, so the members of the churches of Greece and Asia Minor would have been very familiar with how Delphi worked. It was a shrine of the Greek god Apollo. In response to someone's questions, a priestess would go into a frenzy and start babbling. An attendant priest would then 'translate' the babble into some glittering generalities that could in some way be understood as an answer. Some of the best-known features of Greek philosophy streamed out from the Oracle's early years (for instance, it bred the saying "Know Yourself"); the great Greek philosophers were very good at finding jewels in waste water. The cult of Dionysis used rhythmic music, whirling dances, alcohol and/or herbal drugs, and magic spells to send peoples' souls out of their body (Greek ek stasis ) and into the presence of whatever deity or sub-deity was involved; this too sometimes caused strange sounds.
African animists, too, have long had ecstatic speech in their religions. But, just as glossolalia among Jews marked one as a prophet, glossolalia caused most African animists to foist onto the speaker the role of religious leader or priest, a heavy spiritual and cultural responsibility to lay upon an unprepared person. Wherever they have happened in the past, glossolalia and other extraordinary 'spiritual' happenings have not been, and have not really been allowed to be, a thing 'of the people', which could be a part of the otherwise-normal life of otherwise-ordinary people.
Deep in the gnostic book-hoard at Nag Hammadi, archaeologists discovered what may be the earliest, and perhaps one of the strangest, written instances of glossolalia. (Gnosticism arose at the same time as Christianity, and Gnostics were skilled at melding Christian devotions and spirituality to the un-Christian Gnostic framework -- to use a modern term, they tried to 'co-opt' Christianity.) While modern theologians give the unusual contents at Nag Hammadi much more attention than they deserve, a prayer introduction in *The Gospel Of the Egyptians* is a true attention-grabber. It reads roughly (very roughly) like this :
Ié ieus éó ou éó óua! O Jesus, bond of Yah's righteousness, O Living Water, O Child of Child, O glorious Name! Really truly, O Eon that is, iiii éééé eeee oo uuuu óóóó aaaaa, really truly éi aaaa óó óó! O One That Is, Seer Of the Ages! Really truly, aee ééé iiii uuuuuu óóóóóóóó, You who are eternally eternal, really truly iéa aió, in the heart, You who Are, You are what You are, ei o ei eios ei!
Even the translatable words are very iffy and full of vowels and mixed languages. Like modern glossolalia, it's got a lot of almost-words, divine titles, and 'really truly'. It's almost like a parody, it's so garbled, but it was serious in its intent. The ecstatic speech did not make the book's bizarre beliefs the slightest bit more true.