I would notch the wood not the countertop. Wood molding is easy to replace and to work with. I don't think regular tools would work on the counter either.

I've not worked with "cultured granite" before, so I don't know if it's more stone of more resin. ie, do you cut it with a diamond blade or with carbide. And does it cut cleanly, or if you move slowly will you get a bit of melt?

Regardless, I'd pull the side casing on the door, install the vanity, then scribe a cutout on the casing to the edge of the countertop.

So what musicteacher wrote. Notch the wood, not the countertop.

Ok, I know you are purchasing a standard size top. But just in case, have you already measured? It may fit fine. Maybe the current one is 24 in deep. I've seen stranger things in my own home, measuring is free :-)

I'd also notch the wood for my own sanity.