Word-of-mouth leads in Denver after 5 years as a teaching assistant

Two small Denver employers told me they are hiring but have not posted yet. There are 5 people counting on me, so I am trying to be careful. 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 last year, and it got easier once I kept a simple log of every call and form.