I think for a trip to Mars, you'd have to have an orbiting space station where pre-fabricated parts from dozens of Earth launches would be assembled in orbit into a true "space ship".
Either that or colonize the Moon to the extent where you have lunar based manufacturing using lunar raw materials to build new rockets. With less gravity on the Moon to overcome, maybe launches further into space would be easier than something that starts from Earth.
Yeah, all this will require many years and lots of Dollars that we don't have.