This isn't the way house hunting works in most markets today (well, at least up until a few months ago). You need to consider each property as it comes up and decide whether to make an offer or not.

Either you use broad filter criteria and you look at a few houses before you say "this is a better option than what we've seen, let's make an offer". In which case you can ignore the filter for purposes of fitting the house search to the secretary problem.

Or like the parent post, you think you can express what you're looking for exactly through facts that appear in the ads, in which case you look at a few houses, then you buy the first house to appear that exceeds best of what you've seen.

What you do not have in most markets is the option to go back and buy a house you looked at two weeks ago. Houses that sit on the market aren't houses that are appealing to buyers who intend to live in them.