The major private rocket technology companies I can think of that are aiming towards heavy launch capabilities are SpaceX, ULA, Blue Origins. The major gov't space institutions with launch capabilities are NASA?, ESA, Roscosmos, CNSA, ISRO, and JAXA.

SpaceX wants to send about 1 million people to Mars by 2060-2100. I believe SpaceX sending the first few batches of people to Mars will act as a catalyst for other private companies to follow the money trail and for other nation's space programs to secure they place on the red planet.

If those other 9 put together can match SpaceX's pace of colonization, then we can see the "1 million in 40-100 years" fall to 1 million in 20-50 years after the first landing.

It’s not hard to imagine that the nations capable of building an ITS-like ship (Russians, Europeans, Indians, Chinese, Japanese) would send over a few hundred to a few thousand people every 26 months. And then on top of that, we got the likes of Blue Origins and the ULA and maybe a few newcomers that would compete with SpaceX and be sending tens of thousands of people to Mars every 26 months.