How should I approach this ?

So I have 5 years if experience as a software engineer and just got into Google at l3. I should be at l4 but the team I am joining only has opening for this l3 and I took it. My pay is also extremely low because of this (base around 110k).

Should I:

1. Stay within Google and grind my way up (time consuming and no guarantee of significant increase in salary)
2. Switch jobs with another FAANG/Start up after a while to get that desired increase in salary ?

FYI: Google has always been my goal not because of money, but because of the potential for impact. However, being underpaid sucks and is de-motivating.

Ant thoughs?