The best time to start looking for a new, better job is the day after you start your old prior job. In other words, you are never not looking for your next job. Depending on "how good you have it" that may be easier or harder to accomplish. It doesn't mean you have to leave your current team, department, company, or industry. It may be an expansion of your current role, taking on a direct report when you have none, or taking on a direct report who's doing something a little far afield from who you currently manage.
If you're "already gone" and wondering when to look for a position truly outside of your current team / department / company / industry then the best time to start looking is... today. The sooner you start the sooner you'll begin gaining the most valuable resource possible in this scenario: more information! Knowing what kind of response your resume is getting, what roles are out there for you, what companies are interested in you, and what the pay looks like for those roles... all of that is very difficult to acquire absent an actual job search. The sooner you start looking, the sooner you'll have a feel for where your resume and interviewing skills could take you next. Then you can weigh if it's enough better than your current role to be worth it.
If you're "already gone" and wondering when to look for a position truly outside of your current team / department / company / industry then the best time to start looking is... today. The sooner you start the sooner you'll begin gaining the most valuable resource possible in this scenario: more information! Knowing what kind of response your resume is getting, what roles are out there for you, what companies are interested in you, and what the pay looks like for those roles... all of that is very difficult to acquire absent an actual job search. The sooner you start looking, the sooner you'll have a feel for where your resume and interviewing skills could take you next. Then you can weigh if it's enough better than your current role to be worth it.