New Application after offer has been accepted for another

Not impossible but your chances are slim to none.

1. It takes a long time to get permission to fill a post and then identify candidates, if you start the job then leave they will have to restart that entire process. It’s not easy.
2. they will have spent their time to get you here, after selection.
3. They have to agree to release you, so bear in mind the two previous points. In addition to this, the people in charge of this stuff do not like to offend each other. So, it’s not inconceivable that your boss would refuse to release and the new boss would refuse to employ.
4. Huge chance you’d be sent home.