Trending @Accenture; Early release from company with less notice period (within few weeks to a month)

In my current project I don’t have any dependency, anyone can handle the work in team and they can hire people easily for my work. I have an offer in hand and they are asking me to join at the earliest (15 days to a month).

How should I convince my manager and HR to get early release and is there any chances of getting it? I have 35 days vacation leaves to compensate and I’m even ready for partial buyout.

Any quick suggestions would help me!

TIA.