Technically you just need construction to outstrip people looking for homes.
One of the problems is people can move quite quickly from one side of a country to another, it's a matter of weeks. But from empty lot to new house is a matter of months at best, years at worst.
Immigration must be limited to the degree that construction can happen. Because it can be raised almost to an arbitrarily high degree it's very easy to overwhelm domestic home production.
I’m not convinced it’s a problem.
Again, all roads point back to supply. Build enough homes and the issue is moot.