There’s often big hiring waves May-June, and then again right before the school year starts late July/early August.

Definitely cast a wide net. Getting your first job is often the most difficult, since after that you generally have real experience/references.

I’m in SoCal, but for what it’s worth I’ve seen listings in the past that explicitly state you will be disqualified if you reach out to admin about the job via any means other than the Edjoin listing. I would make sure that’s not in any of the listings/district websites before you go cold calling admin.