"Contingent to.." Clause, Two-Week Notices, Relocations, oh my!

[phoenix-]

Hi, everyone. I could really use your assistance and advice. I am planning to relocate to another state and have been applying since I received my license.

I received an offer letter via email from a hospital on the 13th. As usual, there was that dreaded line: "Your offer is contingent upon successful completion of our pre−employment screening process." On the same day, I received a request "to complete my information", ie., SSN, DOB, etc. On the 20th, a representative from HR contacted me with instructions to complete a Pre-Check form. The next day, the same HR representative contacted to finalize my medical appointments, orientation dates and start date.

Here's the trouble. If I am to make it to FL in time for my scheduled appointments and orientation, I have to put in my two-week's notice next week. The only thing I worry about with regards to bg checks is that I did not mention a four-month nursing job I had on my online application because I didn't feel it mattered. I know it's not customary to call the future employee when pre-employment checks are done, but i wish there was a way to be sure this opportunity will not suddenly be taken from me, mostly because I'm moving across the country and can't afford to not have a job.

I know people have done this kind of move before, and I am lucky to have a job lined up while others don't get that kind of privilege, but I suppose I need to hear others' stories, good or bad, that are similar to mine and how you all survived it, because this will be my very first major move on my own and I'm quite nervous.

What are your thoughts? Do you think it will be okay for me to put in my two-weeks' notice? Am I overthinking things?

I'm a little inexperienced with the hiring process within the nursing world, having only done this for the past year and a half. I could really use the advice of those wiser and more seasoned nurses out there. Thank you so much in advance.