1. Clearly communicate with your manager about your promo goals and work with them to make sure you're assigned projects that will help you achieve those goals. Many things related to promo are out of your control, and there aren't any projects that will guarantee your promotion, but you can at least work proactively to avoid missing promotion because you're doing well but didn't have the right projects.
2. Don't work too hard. In my experience, pushing yourself to work too hard has limited upside for you personally. For all its faults, Google is a place where you should be able to succeed without working nights/weekends.
3. Don't get complacent. Google is also a place where it's easy to become comfortable with the status quo. Being comfortable is nice, but don't let it get in the way of your personal development, or impede your growth as a SWE and person in general.
4. Don't be afraid to ask why things are done the way they're done on your team. I think coming in a noogler, one of the ways you can add value to your team from day one is as a fresh pair of eyes on everything. Onboarding can be a daunting process, but don't assume that everything is done the way it is for a reason, and don't assume that you can't suggest a better way to do things.
Also happy to answer any specific questions you have. Good luck!
BTW. Why are you leaving?
I'm leaving for a variety of reasons, but primarily I want a change of pace from big company life (especially during COVID) and want to focus on building my own company (http://trivvy.co/).