The answer is no. Despite the Islamic Republic's animosity towards the US, the American government hasn't engaged in any official or serious effort to change the regime in Iran yet. There have been situations in which Iran and the US were on the brink of war or when tensions were very high, but the United States showed that, despite favorable opportunities, it didn't have any intention to change the regime.
In 1979, nine months after the Islamic Revolution, the Iranian regime took American diplomats hostage. In April 1980, the US tried to release the hostages in a limited operation called Eagle Claw. The operation failed, and the US didn't pursue a more extensive offensive. Given the unstable situation in Iran after the revolution, the regime was very vulnerable.
Operation Praying Mantis: After Iran mined an American warship in the Persian Gulf, the US launched a retaliatory attack, destroying many of Iran's naval assets in April 1988. This battle took place towards the end of the Iran-Iraq War. After eight years of war, the US could have easily overthrown the regime.
After the 9/11 attacks, the US tried to change the Middle East. It changed the regimes in Afghanistan (2001) and Iraq (2003), Iran's eastern and western neighbors, and President Bush designated Iran as part of the Axis of Evil in 2002, along with North Korea and Iraq. After the invasion of Iraq in 2003, it was assumed that Iran would be the next target, but it didn't happen.
In 2009, during the widespread demonstrations in Iran, known as the Green Movement, some American senators, like J. McCain, proposed supporting the movement and regime change. However, the then US government opted for negotiating with the regime, and these negotiations led to the JCPOA.
On January 2020, after the assassination of Iranian general, Qassim Soleimani,got close to a direct confrontation but nothing happened.
But why didn't the US try to change the regime? It is difficult to say. I think the US and the West in general supported Iran after the Second World War, mainly because they needed a strong ally against the Soviet Union. After 1979, they didn't try to change the regime because:
After the Islamists seized power in 1979, they understood that Iran wasn't going to become a Soviet ally, so they didn't need regime change. After 1991 and the fall of the USSR, this danger was completely removed.
From 1991 to 2011, the Islamic Republic wasn't a major problem. They organized some terrorist attacks, like in Lebanon in 1983 with the help of their proxies, without assuming responsibility.
After 2011, the US decided to reduce its presence in the Middle East. This was the beginning of the Syrian revolution. Iran began its expansionist adventures and sent troops to Syria from 2012 to quell protests. After 2015, when the Syrian regime used chemical weapons and crossed what the US had declared as a red line, Iran became emboldened, and after a while, Russia entered the scene, making things more complicated.
In short, the US has not supported any regime change in Iran since 1979 despite constant tensions, and the reason is probably that they didn't see the need for it and thought the consequences of such attempts would outweigh the benefits. Anyway, the US doesn't have good experiences with intervention in Iran. The 1953 coup d'etat and negotiations with Khomeini shortly before the revolution in 1979 have long been the subject of criticism.