We had jet and rocket propulsion tech and physics knowledge. Why couldn't we calculate how to hurl something at the moon and hit it? Plus the military doesn't reveal the level of tech they actually have until decades later. In addition, why did they launch that massive rocket and ship if it was all a hoax? Might as well go for the moon if you're going for all the trouble. Seems like a lot of trouble to go through only for the goal of cheering, "Yay we beat the Soviets!"