By definition a nuclear missile submarine is not an attack sub. "Nuclear submarine" always means nuclear powered and usually connotes armed, btw.

The Soviets outfitted a Zulu with a rather primitive ballistic missile (R-11FM, and then R-13), but at the time they were not nuclear tipped; this was perhaps mid 50s - it took a few years to have enough fissile material and designer warheads for the smaller missiles like R-13. Granted that it may have been 5 years before Polaris - sources, including Russian, conflict on first production and refit - I'm actually inclined to believe that first run was in '58. But there's no direct comparison possible. Remember that the Soviets didn't even have a megaton weapon until right about then, and it took them some time to get it into the R-13s.

Also, I don't think you can compare the lackluster R-13s (look at its service record and limitations) with something like the Polaris, it's a huge leap in technology. That said, R-13s was certainly indigenous - or at least, not borrowed from the Americans as much as Germans - and very much borrowed from the Germans. Also, keep in mind this is a very short range missile, on a short range submarine, that had to surface launch. Even before the Killian reforms the US had an IRBM almost 10x the range. And finally, the US had launched a (non-nuclear) V-1 from Cusk in 47 and Regulus (nuclear SLCM) in 1951. So...

Now, about Soviet military tech reliance on outside sources:

Aluminum & copper tube manufacturing machines, aluminum plated metals and glasses from the US, germanium and valve springs from West Germany, precision instruments, calibrated steel valves, plastic sheeting, nickel wire and bronze alloys probably from Eastern German plants with Western technical assistance.

Check out Mendershausen on this.

More comprehensively, early Sutton is a good read before he was radicalized by his findings.

A juicy source:

U.S. Senate, Committee on the Judiciary, Export of Ball Bearing Machines to Russia, Hearings, 87th Congress, 1st session (Washington, 1961).

Also, take a look at A-12 and Golem 1. As wide-reaching as Paperclip was, the Russians got the best sites minus documents and about 2/3ds of the physical prototypes and specialists.