A quick search brings up:
https://en.wiktionary.org/wiki/Reconstruction:Proto-Indo-European/-t%C3%B3s
(The Greek and cognate forms for participles.)
And this variant:
https://en.wiktionary.org/wiki/Reconstruction:Proto-Indo-European/-n%C3%B3s
Which in fact is cognate with English -en 'strong' participles.

However, looking specifically at English -ed:
https://www.etymonline.com/search?q=-ed
Suggesting it is cognate with the others above, at least as the regular/weak participle ending.
Wiktionary then has three distinct etymologies (unclear whether these might be ultimately related, or if they're intended as compatible but distinct hypotheses):
https://en.wiktionary.org/wiki/-ed#English
There's some overlap, suggesting it may be cognate.

So, as with most questions like this, it's complicated, and controversial. There may be a connection there, but it looks like a complex one. Note that it seems like this is more about participles (adjective-deriving suffixes) rather than past tense, so that is likely the origin, assuming all of this is connected.