The Cold War was a war of propaganda, and the USSR didn't get many propaganda victories. They were doing great in the Space Race, but the Americans eventually 'won' that in 1969 of course.

However, it depends whose side you're on: I imagine citizens in Soviet satellite states were being informed of the USSR's propaganda victories all the time. Like, when the Berlin Wall went up, the USSR claimed that it was to keep out American spies.

Saying this, the Soviet economy was failing big time throughout most of the Cold War. During the Soviet-Afghan War (1979-1989), the USSR economy was drained due to the fact they were constantly being defeated by the Mujahidin who were receiving funding from the USA. The USSR were always competing with the USA in terms of nuclear weapons too: when the USA increased their spending, as must the USSR, so you can imagine the effect this would have on the USSR'S economy.

I would argue that, no, no there was no time the USSR had a strong chance...from a Western POV...

I would say that during the early fifties the tide seemed to be in the Soviets favor. Korean stalemate, multiple communist takeovers of Eastern Europe, Red scare with McCarthy, USSR getting the bombs so fast after the U.S., Sputnik, Cuba and the bay of pigs, and the Cuban missile crisis. After the missile crisis, it seems like they never recovered their lost momentum.