a What if question about the Soviet Union United States stand off

Most likely after the events depicted that there would be a full scale nuclear war and the resultant extinction of humanity as well as most other forms of life on the planet. Basically a shooting match between Omani gunboats and a US navy carrier battle group lead to one of the US ships possibly launching a nuclear torpedo or nuclear depth charge to destroy the Russian submarine that somehow made it through the picket ships (destroyers, cruisers, and frigates that surround and protect the carrier from attack, as well as US submarines that patrol around the carrier), which led to a nuclear attack upon the carrier battle group that destroyed some if not all of the US ships including the Nimitz would be the reason nuclear war occurred. This wanton use of nuclear weapons during a single battle before war was even declared (no matter who launched the first nuke during the naval battle) would mean that already the gloves are off and both Russia and the US would be destroying the other and their allies as best as possible before the same could be done to them (basically destroying each other in the process of attempting to defend themselves). Ignoring the destruction of a whole carrier battle group by nuclear weapons would be impossible for the US president to let slide, especially as the point for that battle group was to defend US interests in the region by keeping shipping lanes open and impossible for the Russians to ignore that the US used nukes to destroy one of their submarines. After the destruction of the Nimitz, the next order the president would probably have is to launch nuclear weapons at the military bases of Russia and Russia would do the same to the US, many cities may be the target too as centers of commerce, transportation, communications, and/or industry in order to disrupt the enemy country's ability to make war.

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