When to start applying for new jobs

Don’t know if this is necessarily the right place to post this. I posted on a page for transitioning teachers too but I know there’s a lot on here that are in the same boat or have sailed to the next chapter already.

Realistically, when should I begin applying for new jobs if I am not leaving my current teaching position until the end of my contract (mid May)? I don’t want to start applying too early and then get offered something before I am able to leave my teaching job. I feel like i’ve seen people say just about everything, from starting a year before to people who started and ended their search in a month. I’ll get paid throughout the summer, so I need a job by the end of August.

Side note: I plan on applying for other professional or office type jobs. Retail/food is not something I am willing to go back into after doing that for years through college. Just for an idea on timeline because, in my area at least, I could get a job in one of those fields tomorrow.

Thanks for any advice! If anyone wants to throw out ideas of what types of jobs I even have a shot at with a bachelor’s in elementary education and 3 years of experience, I will gladly take it.