That is - there was a time when it looked like the USSR was genuinely going to catch up with and surpass the USA, how did they manage this and where did it go wrong?
The USSR did some amazing things, for example in space. That just proves that a command economy can divert investment to specific ends. The USSR narrowly beat the US in several space milestones. We were close behind-such that we beat the USSR to the moon when their space program stumbled. But at the same time we developed advances in electronics, medicine, chemicals, etc., that weren’t even on the USSR’s radar. And we were doing all that while dedicating far less of our economy to investment (versus consumption).
Soviet industry was also breathtakingly inefficient. The USSR required five times as much energy to produce on unit of GNP than the US: http://pure.iiasa.ac.at/id/eprint/3500/1/RR-91-07.pdf. The Soviet Union had massive oil and gas reserves. But using vastly more concrete, steel, and energy to produce less durable goods than the US wasn’t sustainable.
Bulgaria was under USSR's wing when I was a kid, and I have first-hand experience about that.
There was this thing called "kruzhoks", (a Russian word, diminutive of "circle", like in "circle of friends"), which were after-school interest-based clubs, mainly about technical stuff. Every other kid was a member of some kind of kruzhok. Back then I didn't realize that, but the state must have had some sort of "master plan" to prepare as many kids as possible for technical careers when they grow up.
I also distinctly remember the exceptional quality of the textbooks (math, mechanics, electronics). The content was presented in a pedagogical order, with increasing difficulty, and carefully selected exercises that helped the concepts sink in. I used Russian textbooks from the 60's and 70's up until I graduated the university in 2005. (I'm a mechanical engineer, physics hasn't changed much since then, heh.) The typography was also excellent. When I first saw LaTeX output, the first thing that came to mind was Russian textbooks. I don't know how they did it back then.
It was the stagnation in the 1970s where the centrally planned economy couldn't adapt to consumer goods, light industry, and technology where they fell further and further behind. Various incentive problems exasperated things. Things would have been much worse in the 70s if high oil prices didn't mask these underlying problems, allowing the USSR to obtain hard currency to import goods.
Don't get me wrong, communism was bad. However, there were periods where it appeared to look superior. The quality of life in North Korea was "superior" to the south until the late 70s (much of this was backed by soviet subsidies, etc), but the optics still existed. There was a similar, though much more brief, period where east Germany had a faster growing economy than the west. There is a reason the Berlin wall was built in the 60s and not earlier.