

The US is “just” bombing Iran right now. Take for example Pakistan. They launched missiles against each other two years ago. It would be relatively easy for Pakistan to invade Iran and get support from the US and the Gulf states for that. Iran controls some islands in the Strait of Hormuz, which the UAE claims to be theirs. The Azerbijan and Iran also are not exactly friends.
A ground invasion could seriously dethrone the Islamic leadership.


There were a couple of mongol and Turkish invasion, as well as the Islamic Conquest. Last century the Soviets and British invaded Iran rather easily during WW2 as well.
You use helicopters and paratroopers to take an airport close to Theran and then land troops with planes. That is how the US would invade. Iran has lost its air defense, so that is possible.
I honestly have very little doubt, that the US can take Iran, if they wanted too. The issue is leaving it is a decent state after the war. However Israel does not care about that.