Pretty hard to make a center punch in a SS sink without a heavy piece of iron held under it. And any bit not "black" and from china will drill the pilot.
Its no problem to drill a 2" hole in 1/4" steel with a good hole saw if you have oil and experience.
Titanium step bits mean you have to drill several holes, not a good idea for this job. They are made for knockouts for electrical boxes. And the titanium is just a coating over high speed steel [we hope] and essentially a sales ploy.
I would use a lenox hole saw with a flood of drilling oil, or a diamond grit hole saw with a hose on it. Practice on a junk sink.
The secret of drilling holes in steel is enough pressure to get a spiral chip. If you dont get a spiral, you need more pressure . My drilling fluid is the cheapest transmission fluid made, hot water, good soap, and heavy gear oil - used is fine. A little lecithin helps emulsify it when you mix it with a mortar head on a drill.
They sell this 5$ mix for about 80 bucks a 5g bucket. put it in a hose sprayer and use it on your hand tools too.