Nationwide rent control.

We've done it once before (World War 2 - in that case it was even retroactive, so you couldn't hike rents in anticipation), and it increased homeownership rate by the highest rate in the 20th century (something like 5% jump in a few years) by making leasing less profitable than selling.

Would also have to be combined with more building, but it does work. If you make investing in real estate less appealing (via rent control), people will sell - unless they're just hiding money (i.e. overseas investors).

You would probably have to go on a crusade in order to promote it, and it would require a massive anti-landowner propaganda push (of the sort that existed during WWII), but it's theoretically doable.