I don’t think the dates match up.
It is almost for 100% for sure he taught here.
https://en.wikipedia.org/wiki/Capernaum
Most of the stonework is from 400-AD but much of foundations are from much earlier.
The key is there are NO crosses carved anywhere (as this symbol came much later)
All the carvings are done in the Jewish style.
A truly fascinating place to visit.
It has improved much since my visit in 1984, when i could not even find a place to go to the bathroom!
Now there is a beautiful museum over the old foundation, with “facilities”, I assume!
God Bless Israel.