Not before the 2030's. The problem is not just the rocket to get there, it's also due to the astronauts themselves. The rocket will be done in a couple years, but not their crews.
Astronauts will need very specific training for Mars which will be much more extensive than for the Moon because it takes much longer to go there and you have to stay there for much longer before you can actually go back to earth (260 days to stay on the planet on most trajectories before you can go back home to earth). In other words, they need training to be able to live in such a hostile environment for 2 years straight, travel time included.
They will probably also need a constant stream of supplies from earth just to be able to live there, like food, water and oxygen. Starship can transport a lot, but I doubt it can hold enough supplies for an entire crew for such a long time. Which is especially true if they are supposed to build stuff there, something they will have to do or need to be done by robots beforehand to avoid radiation since Mars doesn't have a magnetosphere anymore.
The Nintendo eShop rating Thread: http://gamrconnect.vgchartz.com/thread.php?id=237454
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