There's a good discussion in the thread titled "How much space do you have behind your sink?" that may help you. See the link below.

Here is a link that might be useful: front to back - counter, sink and faucet measurements

You should do the calculation yourself to confirm.

I would assume 3.5" from the front edge of the countertop to the front of the sink. You probably wouldn't be able to get it to be much less, maybe 0.25".

You also need to look at the measurement requirements for your faucet. You will need a bit of clearance between the back edge of the sink and the faucet cutout hole.

You also need to look at the exact faucet and make sure that the handle doesn't have extra space requirements. Some faucet handles extend behind the main tube -- if you are short on space, make sure you have one that doesn't force your fingers to bang against the back wall.

If you have a backsplash behind the sink, you should deduct the width of that material from the overall space requirement.

If your sink is 18" front-to-back you should be able to find a faucet that works, but it will be close and if you pick the wrong one it could definitely be an issue. I would try to find the right matching faucet rather than extend the depth of the countertop, which can lead to other issues (e.g. harder for people to reach the faucet or anything behind it).