Small employers hiring around Pittsburgh after 4 years as a teaching assistant

Two small Pittsburgh employers told me they are hiring but have not posted yet. I have read a lot of threads here and could not find my exact situation. They prefer people who can start within a couple of weeks. What do you write in a cold email?

Thanks for writing this out. I went through something close to it 6 months ago, and it settled down once I kept a simple log of every call and form.