If you are confident that you will secure a job, and don’t have any liabilities on you, I’d suggest to start serving.
For me, I took the shittier route, and absconded after first 30 days of my 90 day notice because the company decided to force me into staying back by withholding my salary (said so in the email as well). Since I joined a startup, I cooked up some story that made me look like a victim, and they didnt care about my previous employer.
See if you can take this route as well, although big companies run heavy background checks, so this might surface