not too difficult.. though it would have to start earlier..
have hitler divide his scientists evenly, the number 1 going to the us, but the number 2 and 3 to russia. the V1 and V2 programs are sent more to the east to forstall the russians with little effect. the russians capture more examples, and the rocket engineers and space programs even out.
Russia still goes up first, but is minutely less capable. so by 1970, they both launch their own missions to the moon. this gives both sides a reason to establish permanent bases on the moon and large space stations.