In SLC? Not likely. The SLC Community college is right on the field, with their aviation maintenance training program, and their students are available for work study or cheap maintenance labor...and get used.
Few if any mechanics can afford to hire an apprentice; you'll need to be working for a shop or maintenance department, and your best bet there is to find a repair station. If you're serious about finding work in aviation, usually it doesn't involve deciding where you'll be living and then finding the work. It usually involves finding work, and deciding that this is where you'll live. Be prepared to move to suit the needs of an employer.