I wonder if it's possible that some of the inventions attributed to China and India today could be tracked to works lost on one of these civilisations collapses.
Then there's the Silk Road who connected the Eurasian continent economic, cultural and political influence for centuries.
So, the spread of ideas across cultures is pretty much established.
The problem is that the survival of specific historic records across centuries or millennia is tenuous at best. First hand accounts are extremely rare and most of what we know about those times was handed down by copying what was deemed relevant throughout time.
Lesson number one each historian learns is to ask critical questions about the source material. Who wrote this? What do we know about the contemporary context? Does other material corroborate with what we are reading now? How about our own hindsight bias when reading records today? What about other biases that played out at the time?
Oftentimes, it's not possible to ascertain a theory or a hypothesis, how things actually went down, simply because we lack the source material. And just as often we may get caught unaware by our own assumptions that were handed down to us by teachers, authors, movies, art,...
As such, most historians will tell you that while it's plausible that the origins of some technologies root back further in time, there's little point in looking for evidence as there is simply no historic or archaeological record available. That's where you'll find that a falsifiable theory turns into mere speculation.
A historical researcher therefore only builds on top of verified sources. Much like a criminal investigator trying to establish the raw facts that support a given narrative.
https://en.wikipedia.org/wiki/Late_Bronze_Age_collapse
The works of Homer, written down much later, are probably based on oral histories of the times before this collapse. There still seems a lot of debate as to what caused this widespread collapse.
What I find fascinating is that there are vast ruins like Gla that aren't even mentioned by Homer that appear to date from just before this time:
You can find temples in Egypt decorated in Mycenean styles. Mycenean style pottery got everywhere. It was very modern.