You could join the Friends of State Archaeology email list. https://www.fosa-ct.org/FOSA_home.html. They have some digs during the summer; right now it’s mostly lab work.

There was a Mohegan field school around New London the past few years, but I don’t know if it will be available next year.

If you have an undergrad degree, you can find work in cultural resource management firms around New England. The work is not necessarily always excavations; they’re probably some Phase I and Phase II jobs though.