Do i have to cut my vanity for my sink trap?
If your shelf is not removable, that  appears to be the case, then you will need  to cut a space out in the shelf wide enough to accommodate the plumbing.
A  Jig-saw will be the best tool for the job.

Is there a way to buy a different p trap so I don't have to cut the
vanity shelf, Or is it the best option at this point?

No, the P-trap is a standard size, The only other option is to cut open the wall and reconfigure the pipe in the wall,  move the sanitary  tee up.(but you have limited space to move it up because of the height of the sink tail piece.)
I believe that cutting the vanity is the best option.