Drain trap is too low for new vanity
No you can't do that.

The P-trap depends on the weir which requires critical trap arm length and a slope that does not siphon the trap dry.  Your drawing siphons the trap.  You could add an aav but opening the wall might be easier.

https://www.jlconline.com/how-to/plumbing/maximum-length-for-fixture-drains_o

The other thing I've done is to make the p-trap assembly in a straight line to the back of the cabinet and then make a cut out in the shelf to accommodate the trap.  I've done this with both drawers and with shelves.