How soon should I apply to jobs in a state I’ll be moving to?

Hi, I recently told my boss that I’m leaving at the end of July and moving to Chicago. I plan on driving there from LA at the beginning of August with my stuff. Which means I probably won’t be available to start until around mid-August because I’d like to settle in once I’m there for about 1 week.

How early should I start applying? Should I start now or wait till end of May/beginning of June?

I currently see multiple positions that I am interested in however I don’t know if I’d be applying a bit too early since mid August is still more than 3 months away.

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