Soldiers stationed in Nazareth in 5-4 BCE

[Nathan Ross]

some people even think it didn't exist

Some people are determined to disbelieve everything they read...

Would near Nazareth, rather than in it, be more plausible?

Still not very likely, I'm afraid. The practice of stationing small groups of soldiers (called stationarii) in towns and villages around the provinces was quite common, especially in the eastern empire - such men did all kinds of things, from local paramilitary policing to directing traffic and maintaining the imperial post.

But this was only done within settled Roman provinces. In 4BC Galilee was still part of a client kingdom; it had no regular Roman garrison, which is why troops were sent from Syria. Perhaps in the aftermath of the revolt small parties of soldiers might have combed the area conducting reprisals and so on, but they would not have remained long in a potentially hostile region.