You’ll get a call for a GS anywhere from 24+ hours out to after the report time of the trip. Generally the more staffed a category is the less likely it is to have long notice as they have enough reserves to cover the trips in open time. Short notice stuff still pops up with some regularity (crew gets stuck somewhere, mx issues, etc, and of course a major driver is wx, primarily summer thunderstorms shutting down a hub for several hours). They may have some short call pilots available to cover last minute stuff, and regular pilots have first crack at any trip via WS before it gets to the GS step of coverage.

Every commute will have a different cutoff time. I’ve made GS trips just a couple of hours from report because I got called just in time to jump on a flight and I live very close to my commute airport. If you drive 60 minutes to your airport for a 1:45 flight you’re going to be much more limited.