The long and short of it is that the Russian navy is a scarecrow. Its big stick, submarines, is due to its incredible geographic limitations as outlined by Anton Gudenus
Probably indefinitely, as all mayor Russian ports are under direct fire control by the US or her allies. Which is also why Russia has such a disproportionately large submarine fleet.
But let’s go through Russias fleet one by one:
- Black Sea fleet: the ships there would never even meet US ships, as the access to the Black Sea is controlled by Turkey, who won’t let them through the Bosporus.
- Baltic fleet: same here with Germany, Denmark and Sweden closing the Sound.
- Northern fleet: they could get out, but would have serious problems getting past Norway and her submarines. And they would have to contend with NATO air strikes from Finnish and Norwegian airfields and being tracked by SOSUS. Realistically the Russians could get some of their submarines out of there without being sunk, but they would then be mostly lone wolfs in the Atlantic Ocean. They might sink a few US vessels, but in the end they would be hunted down and sunk, or surrender.
- Pacific fleet: the situation here is similar as with the northern fleet, though due to the US having naval assets permanently based in the area, here Russian vessels would probably actually meet US vessels in combat during the initial attack. But at the same time the access to Vladivostok is closely controlled by geographical choke points, which are all under US surveillance 24/7, with ROK, Japan and the US having extensive anti-shipping and anti-submarine capabilities aimed at them.
- Russia would probably have a repeat of the battle of the Tsushima Strait on their hands. Though again some submarines might escape into the Pacific and sink a few US vessels before being hunted down or surrendering.
- Caspian flotilla: It would be safe from US attack, but at the same time pose no threat whatsoever to the US navy, due to being geographically isolated.
- Permanent Taskforce in the Mediterranean: Probably also would not meet USN ships before being hunted down by all the US allies around the Mediterranean. They are severely outnumbered at all times in the Mediterranean and also in reach of shore based ASM fire at all times.
And all of this is not even taking into consideration, that Russia has kept its navy in a very sorry state, with most of their vessels being little more than floating scrap-heaps, as was proven by the sinking of Moskva.