There is zero evidence to back up your assertion.

I'm old enough to have been around in the early 90s when the USSR ceased to exist. Russia went into a tailspin for the next 10 years until Putin put a stop to the blood loss. That is - not surprisingly - why a very not nice guy like Putin is incredibly popular in Russia.

So from 1991 to about 2001 Russia was toothless.

In the US we talked about the "peace dividend" we should get from not needing to spend so much on the cold war. There was some talk about ending NATO, but it was very muted and went away quickly. The was NO argument made that NATO needed to stay around because of a threat from Russia.

Russia did not build back enough military might to even talk back to NATO until 2008, fully 17 YEARS after the end of the USSR.

Again, your assertion has no evidence to back it up.