From my understanding, the "cool down" period ranges from 6 months to a couple years depending on performance in an interview. The process for some companies can be very long, much less getting a chance to interview. Refer to some of the threads on Google's placement.

In short, it might be good to start now if desiring a switch in a little over a year. Maybe I have been doing it wrong, but it takes 1-3 months to get a solid initial contact with a FAANG recruiter. Then some of the companies like Google could take 9+ months with interviews and placement. Your experience may vary.

The cooldown period only applies if you get to the very last stage and the hiring team rejects you, I believe. You can ask the recruiter ahead of time as well. You will not be put on a cooldown period from a recruiter screening.