The mythology is that Operation Paperclip gave us a leg up because we got Von Braun. The reality is the Nazis were ahead because they'd poured money into V-weapons and we hadn't. Freeman Dyson pointed out that the war might have had a very different ending if Hitler hadn't wasted more resources on Von Braun than the US spent on the Manhattan Project. But then, we spent twice as much on the B-29 as we did on the Manhattan Project so nothing is straightforward (as per usual).
Fact of the matter is, we did spend $3B on developing a long-range strategic bomber fleet. This prompted Khrushchev to throw money at Korolev because Korolev promised Khruschchev ICBMs. Throwing money at Korolev gave the Soviets a leg up temporarily because the United States was too busy developing two parallel rocket programs (Von Braun at Redstone Arsenal in Alabama vs NACA), one running kerosene and the other running LOX. As soon as the Soviets embarrassed the United States, we merged it all into NASA and the Soviets proceeded to lose as big as a struggling command economy could be expected to while facing down the never-invaded winner of the world's largest geopolitical conflict.
Matt Brzinski's Red Moon Rising is about exactly this.