Quantify in my opinion requires qualify because, how many is "a lot?" But broad strokes, the USSR was an intellectual powerhouse. Add as many "in spite of"'s as you like, but in my opinion the "a lot" target is achieved. You mention science and I'll get to that, but I want to first target what I feel is a general misconception of the Soviet Union as like, a bleak concrete-ridden, muddy backwater of labor camps (it kinda was of course) with nothing to contribute to the world.
Post revolutionary periods always produce fantastic art, literature, and social experiments. See post-revolutionary American religious scene for an example. In the Soviet Union, there's a clumping of great literature around 1917. Summary: https://en.wikipedia.org/wiki/Russian_literature#Early_post-...
> The Imaginists were post-Revolution poetic movement, similar to English-language Imagists, that created poetry based on sequences of arresting and uncommon images. The major figures include Sergei Yesenin, Anatoly Marienhof, and Rurik Ivnev.[65] Another important movement was the Oberiu (1927–1930s), which included the most famous Russian absurdist Daniil Kharms (1905–1942), Konstantin Vaginov (1899–1934), Alexander Vvedensky (1904–1941) and Nikolay Zabolotsky (1903–1958).[66][67] Other famous authors experimenting with language included the novelists Boris Pilnyak (1894–1938), Yuri Olesha (1899–1960), Andrei Platonov (1899–1951) and Artyom Vesyoly (1899–1938), the short-story writers Isaak Babel (1894–1940) and Mikhail Zoshchenko (1894–1958).
Sorry for the big copy paste, but, there's just so many of them, and to literature nerds, what they did was "groundbreaking." I know it sounds silly but let us literature nerds have our thing.
Then there's a bunch of fun leftist / communist poetry, from Vladimir Mayakovsky and Nikolai Tikhonov (the "Could nails from such people be fashioned" guy).
And on and on. Art had some interesting characters as well, "in spite of" the Socialist Realism thing. Isaak Brodsky, for example.
Re: science, as someone else linked, efforts were hampered slightly by the repression of science that was perceived as in opposition to dialectical materialism, but in general the Soviet Union seemed very determined to create a lot of engineers.
You have Fields medal winners: Grigory Margulis (interestingly he suffered from the Soviet antisemitism mentioned in this article), Vladimir Drinfeld, and Sergei Novikov. And you have nobel prize winners such as Nikolay Semenov, Nikolay Basov + Alexander Prokhorov, Pavel Cherenkov (the Cherenkov radiation guy) + Ilya Frank + Igor Tamm, Leonid Kantorovich (basically invented linear programming), Pyotr Kapitsa, and Lev Landau.
Then there's the obvious such as the fact that the Soviets were first to put a satellite in orbit, first to put a human in orbit (arguably far more useful than putting a human on the moon, though putting a human on the moon is probably more inspiring).
What is interesting is how during the time these may not be "contributions to science" due to the USA and the Soviet Union often not sharing advancements in science with eachother because of the Cold War. Imagine if the two nations had been cooperating with eachother. Then again maybe there wouldn't have been a "Space Race."