Catholic ping!
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.
Just as a clarification to those who may be confused: the Eastern Catholic churches are separate from the Eastern Orthodox churches. The latter is not part of the Catholic Church and is not what is being described in the OP.