I don't think it is possible. The only way you can leave without hurting both side is that you cut short the notice period by pay in lieu, pay the balance of your working days with cash.

So the question here is, can your future company pay the balance in lieu for you or you need to fork out yourself? I have friends who had a company that wants her so bad, the hiring company pay the balance of the in lieu for her so that she can start early.

You need to talk to your future company, see if they willing to take this move. Else you need to pay by yourself.