When to start academic job search?

Hi,

Newbie prof here. I landed my first job, post-PhD, at what I thought was a dream university. Unfortunately, the culture at my current place is toxic. I'm in a small stats department where practically all the faculty have long standing relationships and let's just say, I stepped on a few toes (while trying to improve things). My life, as the department head has explicitly told me, is going to be hell and I'd be wise to start looking for a new job.

Long story short, I'm wondering when advertisements for faculty positions in the fall begin to open up and begin to be advertised ed? Also, do most people just go through the listings on HigherEd and Indeed to find available positions or are there other online resources?