There are many answers to "how do others do it". But for the first problem, accumulating a down payment, it all comes down to gross savings rate. What is the guideline for mortgage payments in Canada now - maximum 28% of gross income? Serious home seekers have to be hitting that number at least and I suppose should be targeting more if working on a down payment. Minimizing rent cost in the meantime is the challenge.
Car ownership can be a real sink. I've owned 8 vehicles over my 40 adult years; including the ex's contributions, the total purchases prices sum up to somewhere between $50K and $60K (one was purchased new). I'm sure I managed to not spend a lot on cars; I know people who drop almost that much on one car.
Part of the problem is how homes are built now. There are some places where the underlying land is so expensive that the construction cost is fractionally less important, but no question that a rectangular 1600 sq ft box with one roofline, an unfinished basement, and a carport is cheaper than 2400 sq ft with bay windows, fake gables, well-appointed interior trim and finishings, and a two- or even three-bay enclosed garage.
The chief problem is simple: more people, same amount of land. Pick any major city, find old skyline pictures and compare to now.