In 1956's, The Exporation of Mars, Willy Ley explains that in order to reach a far celestial object like Mars, a heavy lift rocket like this one by Bonestell must first be developed.

First, such a lift rocket would would be used for satellites and smaller payloads, which indeed happened in real life- from the R-7 to the Saturn V.

The third stage here, in a Mars mission, would be the Mars spacecraft.