>>7620240There could be men on Mars in 2020, 2018 if they wanted to really push it. It wouldn't be very comfortable, but one or two guys could just ride a Dragon V2 launched by a Falcon Heavy to the Mars surface. Four could ride it down with a separately-launched inflatable hab (mission assembled at L2).
Most of the difficulty is in bringing them home, and that's something that simply doesn't have to be done. The plan could be Mars-to-stay, or at least Mars-to-stay-for-a-good-long-while, until enough of a base is developed to support fuel production and launch home.
I don't think it's likely to be this rushed, but it could be done. One or two-launch test/prep run in 2018, min-four-launch manned mission in 2020.
The BFR/MCT could be running by 2020. The first manned Red Dragon could go alongside the first MCT. If the MCT landed well on the first try, it could be used as a return vehicle. If it didn't, the astronauts would just have to do without its massive load of equipment and wait for the next window (probably without a lot to do but eat the supplies and change out filters).
Once MCT is proven, they could start sending a dozen guys at once, and work their way up to sending a hundred at a time as the crew-equipment ratio improves with the establishment of self-sufficiency. Serious colonization could start as early as the 2022 window, with the first colonists landing in 2020.
I'd like to emphasize that I don't think it's likely. It's just possible.