Google UX L4 > L5

Fairly new to Google and coming up to my year and a half. Hired as an L4 Interaction Designer in a Southern California. Was going for L5 during interview but leveled at L4. Made it a point with my manager since I started that my career goal was to whatever I needed to do to get to L5. I got CME first review cycle, and EE this past one, but then we changed to GRAD and manager said they are still trying to figure it out. He mentioned that we can try to go for promo in the next cycle (March 2023) which I am cool with, but most recently said that we should wait until end of year 2023 to go for promo. That would put me at nearly 3 years at L4 before I get the chance to up for promo. He said trying too early for promo and not getting it would hurt my chances for the next cycle. That seems too long, where I could try my chances at Apple or Meta for a higher level in that time. How can I bring this up to my manager that I am interested in still trying for promo in March 2023 instead of EOY 2023 without seeming desperate for a promo? Any stories of people going through similar timelines? Any advice or suggestions? YOE: 8 TC: $237k Location: Los Angeles