Also, if i made the 1/2” cut i would have roughly 3 3/4” from the front edge of counter to the inside of the sink.

"Can i cut out a 1/2” recess in the top rail (shown in picture) to gain that extra space?"

Yes, no problem.

If the sink material is cast uron, you can seal the raw metal with an epoxy paint. Couple coats.

dan1888:

The sink flange can probably be trimmed, but it's less risky and easier to cut the wood top rail of the cabinet to gain the room for the faucet. The rear sink flange can be drilled for the faucet hole if necessary.

Is that sink porcelain over cast iron?

Whatever material that is you are going to risk chipping, You can't use a ole saw, so you are probably looking at a grinder of some sort or a small cutoff wheel. Cast iron is difficult to cut. Curves are difficult to cut.

Cutting o the sink is a BIG RISK and not advisable just due to the material. I'd be more comfortable if you needed to do an entire hole, vs just a curved area.

Cut the cabinet