I bought a house within 3 weeks of starting a new job in 2013. The bank wanted a copy of my contract, and then when we were closing they wanted a copy of my first paystub, which I was barely able to produce, as I got my first paycheck around a day before we closed. I recall that they were not so concerned about me having a new job, but they were concerned about me being in the same career.
I'm very hopeful to get a job offer in a new state soon enough, and hope that I will be buying a new house in the new state prior to starting the new job, and after quitting the current job. We'll see how mortgage approval goes. I now have more assets than I did in 2013, so I'm anticipating it will work out. In 2013, my networth was -150,000. Now it's +1,000,000, but a good 650,000 of that is in 401ks/Roths/HSAs, so I'm thinking it will look good but not sure how much it will help.
Good luck!