Trending @Cognizant; Bench & Resignation queries

Hi all, I'm a PA level employee. I'm currently on a billable project. I've got an offer from a company but they want me to join as early as possible. If I ask for a release from the project, they will release me after 30 days. And then I'll be on bench. My query is: If I put paper when I'm on bench, will the HR allow me to get released from the company in 2-3 days? Or on whom it will depend on? Because I really want to join this new company. Please suggest all the possible ways of resigning early from Cognizant.