How early should you start looking for jobs?

I plan on leaving my current job in the beginning of July. To be proactive, I’ve been applying here and there and I have interviewed at one job, but they needed an immediate fill. Should I slow down on applying since July is a bit far out? How many months before a goal start date should one apply for a new position? I know it’s very unpredictable but I’d like to be respectful of both my time and a potential employers.

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