Possibly there need to be some definitions here in 'Conquer Mars'. Humanity has had the capability since the Apollo program to fly a small number of people to mars, land them there and maybe even get them back home as long as a large enough pile of money was available (on the order of the entire Apollo budget per mission, but less than US GNP).
This concept is the focus of current planning and with time/tech advance reducing the 'pile of money' to something a private enterprise rather than a nation might have access to.
For this the faintness of Mars atmosphere does not matter since there is still 25 teratonnes of it to harvest for a temporary base of no more than 100.
The next hypothetical step would be building a base of <100 into something vaguely self sufficient, with population in 10ks but still living inside cans and for this there is still plenty of O2 available in total.
Some very rough math at 1kg of breathing air per cubic meter and a 2 meter ceiling height gives a total living/plant growing area of 12.5 billion square Kms if you harvest the entire atmosphere, where total Martian surface area is 144 million. So the entire surface could be built over with sealed habitats without running out of gas volume. The gas mix would be a problem and building to this scale would run out of nitrogen and almost certainly other materials critical to life and technology. For example Helium collection is a byproduct of natural gas extraction and may be vanishingly rare on mars.
Where the total atmosphere quantity starts to matter is in terraforming, turning mars into something where you can live without life support. As you note this would require getting enough gas into the atmosphere to at least stop life getting freeze dried, and plans for that generally include relocation of mass to take the atmosphere from 25 teratonnes to something closer to earths 5000 teratonnes. Any plan to do this will require massive amounts of energy, noting that total human effort to date has got 'only' 8000 tonnes into space, and this mass would most likely be coming from Jupiter or even further out.
So conquering mars as a cities in a bottle is very hard but something where at least the problems can be understood using today's tech. To conquer mars to the point you can walk around outside in shorts the best guesses that can be made today is that the time scales will be in human life times, and involve energy production measurable in % of total sun solar output.