99% of humans only can live off the land because of technology. Most of the US would die tonight without man-made heating, clothing, and shelter. Mars would require different technology, to be sure.
> For colonization to work, it must be self-sufficient nearly from day one
Why? The American colonies did a lot of trade with other countries. They have never been "self-sufficient."
A Mars colony would need to place priority on low-density objects, like generating their own food and water. We obviously haven't done it yet, but we don't think it's impossible. They would still use trade to get in very wealth-dense things, like nuclear fuel and computer equipment for a while, but that doesn't mean that they would necessarily be charity cases.
The first colony in Australia nearly perished through hunger but was saved by the arrival of a second fleet of ships, but who themselves had suffered the loss of a supply ship in bad weather. It wasn't until the 3rd or 4th fleet of ships that the colony even started to move away from borderline starving.
A common strategy for Mars missions is to send the supplies there first. You can land habitats, vehicles, food stores, water-producing machines, power plants (and the return vehicle, if we're not talking about one-way missions), and check on them via radio before your crew ever takes off.