Have used maybe 2 cheques, bought a condo share but a house is a whole other matter. That said I don't think it's impossible, the main issue is just stability, if I had a partner who earnt as much then it would still be tough but not impossible.
But you can absolutely own your residence OP - just look for smaller places, in cheaper areas, and jobs that would offer a good salary : cost of living ratio. You'll probably have to start with a condo in a HOA, etc. but that's better than renting.