Competing offer to boost TC

I recently <4months joined AIML, ICT4.
I did not negotiate on my Apple offer and I know I am below the avg comp band.

Question: Before my next review can I bring this up to my manager saying I need a bump? If so when should I (what time of the year)?

My previous employer also wants me back and is ready to exceed Apple comp. I can also get a competing offer to exceed my current comp.

I prefer not to leave Apple because the work is interesting and I don’t want to burn bridge with Apple.

Has anyone done this? Has it been successful/failure in the long run?

TC: 310k
Yoe: 6 + phd