Some questions for you to consider.

[MistressEll]

Same smelly if using all cold or all hot water?

Is this sink the only location you have the smell?

If you plug the sink bowl before you turn on the water – do you still get this smell when you first turn on the water?

Did you forget to install a P-trap for the new sink?

Try taking some pipe cleaners to the overflow running them down to towards the sink’s drain. If you get a lot of slimy goop – it might be bioslime in the overflow – might not have lined up the drain assembly correctly with the overflow drain hole.