New jobs

I’m having a bit of a crisis. I recently for quit my job for a few different reasons, mostly that I was never trained properly, and that now effects how people treat me in the office and it’s gotten to point of harassment and I really just want out. But I know if I quit with no notice, the next person with my job will just have the same problem. I’m really the only people who knows how to to my job in its entirety. So, without me, the next person will get the same half assed training I got, and end up in the same situation I’m in now, in a year or so. I don’t want to have what is otherwise a fairly good job, go through this cycle. I decided it was time for me to move on and find something better so I put 2 months notice in. My friends and boyfriend have told me this is more than they deserve but I know leavening last minute won’t effect the people who treat me poorly, it will come down on my coworkers who don’t.

Fast forward 3 weeks, I am looking for jobs and have an interview. It goes really well, I like the people, like the job etc. and I’m pretty sure they’re going to give me an offer. The thing is they want me to start in 2 weeks but there are still 5 weeks left of my notice at my previous job and they have yet to even start the hiring process, let alone start training.

How do I cut my notice short if I get an offer from somewhere else?