I don’t think there could be such a thing as an “archaeology firm”. Generally, archaeology is pure research, and is conducted through universities or possibly governments, not by companies for profit. If there is a university near you with an archeology department (or an anthropology department in which someone is doing archaological research), perhaps you should try to contact a professor there. You could probably find one willing to meet with you to discuss career options.

There are archaeology firms that do it for profit actually (and at least in the UK there are companies that have their turnover in millions) and they do hire geophysicists. I don’t know where you stay, but I can talk about it from the UK. (since that is where I am)

Companies here do tend to have either one or two in their staff or alternatively I do know of people that are hired by archaeology companies on a freelance basis, but clearly you would need all of the different machines and software to do this. The work that they do within the company is to survey sites before excavation or even to assess sites that may be developed in the future. We have used them to do work on protected sites to find out the extent of the archaeology and also to find out the kind of depths it is at to then see if the site is at risk.

There are less of these positions than normal archaeology jobs, but what I would do is to look at volunteering for a bit with a company to show what you can do and this can get your foot in the door as well as let you build up your experience actually in the field.