Trending @Capgemini; Navigating Notice Period Challenges: Seeking Advice

I’ve been working on the same project for 2 years, and it’s now in the release phase, set to end in a few days. I've received a new offer from a different company, but there's a 3-month notice period as per their policy. Since I’ll be on the bench soon, should I ask HR for a quick release, or should I serve the full notice period? Any advice would be appreciated!