As noted, explicit references to the Babylonian Talmud from other texts provide an upper boundary of the early 8th century on when its compilation can be dated. The very earliest manuscript fragments of the Talmud, from Cairo Geniza, also date to the 8th century. But we can be more precise. The Babylonian Talmud dates to somewhere between the 6th century to the early 7th century (before the Arab conquests). This is shown by Monika Amsler, The Babylonian Talmud and Late Antique Book Culture, Cambridge 2023, pp. 122–123.
While earlier scholarship tended to place the date of a “final
redaction” in the mid-sixth century based on medieval pedigrees of
talmudic sages, some recent scholarship has assigned dates ranging
from the mid-seventh century to the second half of the eighth
century.54 The latter dates would imply that the Talmud was written
down and redacted after the Arab conquest of Mesopotamia. The
assignment of a date after the Arab conquest is contradicted, however,
by the fact that the Talmud does not contain Arabic loanwords or
syntax.55 Such loanwords should be expected to be found in a text that
went through the last stages of oral transmission after the (final)
Arabic conquest, or at least in the notes added by the final
redactors. Arabic as the new lingua franca was widely embraced, and by
the tenth century, even the non-Semitic Persian language used 30
percent Arabic words, while Aramaic had completely disappeared.56
Texts authored by post-talmudic rabbinic sages (Geonim) were
exclusively written in Arabic by the eighth century. This would point
to a terminus ad quem for the composition of the Talmud in the early
seventh century.
Just for context, I will also quote Amsler's compilation of earlier opinions about the dating of the Talmud:
On earlier scholarship (e.g., Isidore Epstein and Hanoch Albeck), see
Günter Stemberger, Einleitung in Talmud und Midrasch, 9th ed. (Munich:
C. H. Beck, 2011), 215. Charlotte E. Fonrobert and Martin S. Jaffee,
introduction to The Cambridge Companion to the Talmud and Rabbinic
Literature, ed. Charlotte E. Fonrobert and Martin S. Jaffee
(Cambridge: Cambridge University Press, 2007), 9, give the seventh
century as a closing date for the Talmud; Richard Kalmin, Migrating
Tales: The Talmud’s Narratives and Their Historical Context (Berkeley:
University of California Press, 2014), ix, reaches the date 651 CE;
David Weiss Halivni, The Formation of the Babylonian Talmud, trans.
Jeffrey L. Rubenstein (Oxford: Oxford University Press, 2013), xxix,
moves the date back to the second half of the eighth century. See also
Halivni, Formation of the Babylonian Talmud, 9, for the length of the
period during which Halivni conceives of the Stammaim as being active. (pg. 123, n. 54)
Another way to narrow down the range of the Babylonian Talmud, other than that it must have been before the Arab conquests, is by pointing out its reliance on earlier texts that we can also date. For example, Amsler shows that the Palestinian Talmud, which we know the Babylonian Talmud relied on, must date between the late fourth century and the early fifth century (Amsler, The Babylonian Talmud and Late Antique Book Culture, pp. 127–131). This page also contains more information on how the Palestinian Talmud is dated: https://en.wikipedia.org/wiki/Jerusalem_Talmud#Contemporary_views
Therefore, the final compilation of the Palestinian Talmud also gives us a lower boundary of when the Babylonian Talmud could have originated.
