Take Columbus era exploration. It was started by "the crazy ones" who took ships out to the farthest extents of the oceans to see what's out there, simply satisfying their curiosity. It was fueled by wealth (literally, these were funded expeditions!) and the goal was to reach faraway lands and bring back gold, spices, and what not.
A lot of amazing work gets done when you have two competing giants. Sports teams are the typical example, where two cities and their respective teams train and fight hard in order to beat their others. The Moon and the Cold War is a more productive example. Most, if not all, space technology was funded with the purpose of achieving a military strength over the enemy.
What's going to be the Martian story? I imagine Elon Musk is one of those "crazy ones" who will get to Mars purely out of curiosity and ideals to become the first known multiplanetary species. For any of your terraforming and colonizations dreams to come true, one Elon Musk is not enough. It takes an entire society to band together to do so, requiring us to reprioritize our budget and focus all of our resources on colonization.
The best thing would be to invent an alien attack. Fear is a strong motivator. It will likely accelerate 50-year research projects into a 5-year schedule.
A more realistic and albeit less exciting route would be to discover rich mineral deposits of rare earths.