Preventing toothpaste residue in sink

Clean it more often? If you've got that much build up you're talking months without cleaning it. Try cleaning it every single week with surface cleaner, a scrubbing pad, and some elbow grease and see if the buildup is still there.

Boiling water, soap, and time?

I’m struggling to take this seriously though. Looks like a satellite shot of the moon.

Are you positive this is toothpaste and not hard water stains? Do you have well water instead of city water? Do you have a softener? Does it have salt in it?

Maybe my screen is too dim right now, but I straight up thought this was the moon

Wear a plastic face guard. the build up is literally tiny particulates flying out of your mouth while you brush. just wash your counter after you brush is basically the only way.

I'm guessing the material of your sink is rougher and not smooth like most sinks which causes this?

In that case, be a bit careful, as some chemicals have a tendency to react and stain or even ruin certain materials like natural stone.

That said, I would guess that what is left over is likely calcium based. In that case you could try treating it with a softener/calcium stain remover that you'd usually use to treat hard water stains.

Again, make sure to check if the material you are using it on is suitable.

Very helpful responses - will give some of these options a try - thanks!

not a preventative but I would use a larger brush to make it faster. like standard scrub brush.