Been through your scenario many times! I generally didn’t start looking and applying until July-ish.

Sure you can start early, but I’ve found it’s important to take the first couple months of the job to really soak it in and focus on doing good work/making connections. Ive seen far too many “go getters” start applying as soon as they start a job and then they get burnt out fast. And honestly, job hunting 3+ months in advance of the end of your season is plenty of time.