What would be the definition/timer period of "Apostolic Times"?
There's a larger sense which would include the Apostolic Fathers, that is, the first-generation disciples of the Apostles, those who learned from the Apostles personally. That would extend the time-frame by a generation: AD 33 - AD 160 or so.
This list shows the span:
There are also writings on the catacomb walls, monuments, ossuary inscriptions, and --- importantly --- music (meaning songs, hymns, chants) which for many communities was important in the transmission of the truths of the Faith.
I wrote a little about that HERE (LINK) a few years ago here at FR
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In the Apostolic Age there were few books, but many communities where psalms, hymns and inspired songs (very often containing verbatim Scripture) facilitated the memorization and internalization of the basics of the Christian Faith which the previous generations had learned from the Apostles.