What is the best process? Do I accept job and then negotiate leaving
time with current boss? Or do I negotiate leaving time with my boss
before accepting the job?
You accept the job but tell your new employer that your current company requires a 3-month notice. If 3-month notices are standard in your part of the world they should understand, even though they would prefer that you start in 1 month.
You also tell them that you will attempt to negotiate an earlier leave date if possible.
Then, you talk to your current boss, give your notice, and attempt to negotiate an earlier leave date.
Once you and your current boss have agree on a leave date (early or otherwise), you inform your new employer of the anticipated start date.
Finally, you work your notice period to the best of your ability, leave, and join your new employer.
If for some reason your new employer absolutely will not hire you unless you can start in 1 month, you may be out of luck. You could choose to attempt to negotiate an early leave from your current employer without having a formal job acceptance, but that could be very tricky. Likely it won't come to that.