First, I'd like to apologize if my questions come off as naive. I graduated 15 months ago and I'm new to having a career.
I've just started a job at a university in Florida, which makes me a state employee. A few weeks after starting, I received an offer from the company I really wanted to work for, but didn't get back to me in time. I really want to take this new offer, but I'm concerned leaving after a short time (one month) will hurt my chances of getting another job working for the state.
So my questions are:
Will leaving my current position after such a short time make it harder for me to get another state job (like another university) in the future?
Can prospective employers see all the places I've worked (even the ones I've left off my resume) and how long I've worked there through background checks?