Aren’t large ship in a small pond like ducks?
It depends.
Were hostilities to ensue the CVNs will head outside the strait and linger about 100 miles out in the Arabian Sea. While air dominance is being established the US Navy would likely be replenishing the empty tubes of all escorts...refueling...
During this time there would be 2-3 subs in the Gulf along with a Surface Strike group of 4-5 Aegis Destroyers/Cruisers.
Ships today are far, far more capable than even 20 years ago. Think of them as spaceships with a bunch of very precise ordnance and sensors to support it.
For several days...as long as it took...they would undertake strike operations against targets that could restrict shipping and any supporting targets that could present a threat to these strike operations.
Then the Mine Sweeps will commence.
Entire duration: 15-20 days. 20 - 30,000 dead Iranians.
Welcome to Maritime Operations 101. This will be a challenging, but interesting course.