Can someone please help me with suggestions.

I need to get an early release from cognizant, my project ended on 30th April 2025 and since then I was on the bench till 28th May 2025. I was looking out for job opportunities outside the organisation I thought if I am not tagged to any project I will get early release so I informed the same to the interviewers and so I am almost getting offers from 2 companies but now all of sudden they have tagged me in project for which I just randomly gave an interview.so the question is how will I get an early release if I am tagged to a project recently like yesterday only, will the HR agree? is there a way out?