I don’t think the issue is so much whether the free market “could” produce space travel, but rather if it “would.”
Remember, the free market is designed to fill the most urgent needs of individuals, not the arbitrary demands of governments. So, for example, I would say that the free market *could* have produced the Apollo Program and landed on the moon, but they didn’t, because landing on the moon was not economically viable, presumably because it wasn’t a very urgent need of many individuals out there.
While the resources of the free market are vast and *could* be used to meet almost any challenge, I don’t think the free market will necessarily be all that interested in sending a bunch of people to Mars until they figure out how to monetize it somehow. Going to Mars is not very high up on most people’s list of priorities.