Yes, what you're postulating is certainly possible. However, for many of the oldest continuously inhabited places there isn't a written record, but there is an archaeological record. In some places like Matera, Italy, evidence of stationary habitation dates to the paleolithic.

It's near impossible to find villages or small towns that have lasted farther back then the Roman Empire. There are virtually no records kept of smaller villages, so it's hard to find written evidence. Most villages that have lasted for thousands of years are either destroyed/abandoned before they last that long, or become larger. For instance, the city of Lebanon has been around since around 3000 BC, but before that it was just a large settlement. Even Beijing's caves were inhabited by Paeleolithic people's from 27,000-10,000 BC before it became a larger city. Like the other comment said, villages like Mantera are as far back as you can get for continuously inhabited villages that stayed as villages.