The Soviets had a very active rocket program from the early 1930s onwards, with a great deal of work being done in the early 1930s in a wide range of subjects. To quote Siddiqi again, "in May 1935...RNII [the Reactive Scientific-Research Institute, the principal government research institution into rocketry at that time] was divided into four major sectors emphasizing solid-propellant missiles, [JATO/RATO-type units, also solid], launch installations for solid-propellant rockets, and liquid-propellant missiles" and "[Korolev] found himself [at about this time] leading efforts on a number of promising long-range winged missiles for military applications." In other words, they were considering vehicles similar to the A4 and A9, though not developing them to the flight level, of course. They may have been considering more advanced solid-fueled rockets of a similar capacity (and certainly were by 1944, per the above quote; with a range of 115 km, the longer-ranged of the two previously mentioned missiles would have had about half the range of the V-2). It would be rather interesting to consider an alternate timeline where RNII wasn't broken up by the Great Purge and invented composite solid rocket fuel independently from JPL (which developed it IOTL) before the German invasion, as one of the most distinct differences between Soviet and American rocket designs was the fact that the latter preferred using solid rocket boosters for high-thrust applications and in ballistic missiles, while the former preferred liquid rockets (though that's a bit beside the point).
In many respects they paralleled the Germans exactly (one reason why, to paraphrase Siddiqi once again, the Soviets only got management techniques from them), but their poorer industrial and technical base and, critically, the Great Purge (which targeted RNII heavily due to its connections with the military) delayed and dented their efforts, preventing them from developing rocket technology to that level until after the war. Nevertheless, they were fully capable of doing so and had, as demonstrated, several pre-war efforts in that general direction, which would likely have born fruit with the development of the nuclear bomb if there was no German program.