I'd find a really small vessel sink and deck mount a single hole faucet off to one side rather than mount it behind the sink:

Thank you. Desperately trying to avoid that as already have a spread faucet that matches all the other hardware in bathroom and it will look horrible and off balance on the side of the sink. But maybe no other choice.

Edit- so I this brand does make a single mount also, would this work aesthetically with an undermount oval sink off set to the side as well?

Something small w/ faucet hole integrated into the sink like this

https://www.duravit.us/products/all_series/happy_d2.us-en.html?product=1141853

Have the local skilled fabricator create a small custom integral porcelain slab sink, similar to Roberto Colonett’s work here. Or a Corian fabricator, if there’s no porcelain one available.

https://www.colonettiroberto.com/gallery

Return the faucet you have and buy the single hole version and mount it to the side. The one you have won’t work. Since the cabinet is already built it’s probably too high for a vessel sink.

Good point on the cabinet height @Hallett & Co