What you're getting at here is that there is no actual cause-and-effect testing in social sciences because there are no actual controls. And that's true.

On a micro-level you can get pretty close with SRS cohorts where as man variables as possible are controlled for. So if a grocery store in a particular neighborhood changes its policies, you can get a pretty good idea comparing Group A in the neighborhood who shops at that store and Group B who shop at a competing store.

But when you get to more macro-level issues that involve large populations with different cultures, histories, and values it's impossible to actually determine the cause(s) of a particular effect. A change in behavior in the USA in 2018 because of some particular thing does not necessarily translate to a change in behavior in Malta in 1847.

So the Austrian approach is to posit behavior from first principles about human nature. People act. Those actions are in accordance with their subjective goals (this is how they define rationality). Note that there are economists who disagree with these suppositions.

It gets immediately complicated because people are working with incomplete information, maybe they have bad strategies for achieving their goals, maybe their goals are pretty bad goals in the first place, etc etc.

So in your example of a housing shortage, we'd have to look at people's desires to have housing with their subjective values. Then look at the economic environment in which those people are acting to see how choices might be influenced or constrained.