There is a good amount of entry-level positions in archaeology in the US, largely within the compliance sector (this includes Cultural Resource Management or CRM companies and government organizations such as the National Parks Service). Typically, you need a Bachelor's degree in Anthropology and an archaeological field school under your belt to be a competitive job candidate. Your employment opportunities will broaden significantly if you are willing to relocate. Generally speaking, you start as an archaeological technician and can move up to a Crew Chief if you are a reliable employee who can operate independently and who works well with others. The job usually entails travel for fieldwork, working outdoors in all sorts of different weather, sometimes mundane office or lab work, and a LOT of paperwork. It isn't for everyone, but I've found it a rewarding path.
Best of luck to you!