Personally I don’t like quitting commitments, but I’m very careful about making them in the first place. (This is why I’m a remote consultant...)
When you started, you must have had a reason for joining. What was it? Is it still a valid reason, or has new information changed your perspective?
My advice: finish the year of residency, and apply to other jobs just prior to finishing it. If you time it right, then when you get the promo offer you will have other options to compare it against. Also, I just googled this program. I didn't realize it was for engineers in their early career. In that case, I definitely encourage you to wait for the promotion, take it, and at least work a couple months there. Otherwise it might look like you left because you weren't offered the promo. Not sure on that though, I'm not a hiring manager.
Regardless, I don’t see a reason to quit without other options lined up. You can easily find other options while employed, it’s not like you need to quit first.
Also, it’s google. Not the worst place in the world to spend a couple months coasting as a corporate drone.