I bought a 100k house 4 years ago with about 13k in down payment+closing costs. Yes I live in a smallish town and that comes with some compromises, but it is an option that exists for people. With the subsequent boom and then normalization of house prices my house has gained about 40k in value, so where I closed with a purchase price of ~120k, it's now showing a value of around 160k (and peaked around 180k a year or two ago)
There's also plenty of large and major cities with home values of around 200-400k if owning property is your long term goal. Quite frankly if that is your long term goal there are options. Maybe you buy a fixer-upper and invest a bunch into repairs and renovations over time. Maybe you have a friend or two you can have join you in a purchase to increase your buying power. Maybe you buy a duplex/multifamily home with a friend or 3. Maybe you buy a duplex/multifamily home and rent out the other units to strangers. Maybe there's a nice place where you can still commute into your city where home values aren't outrageous. Maybe you know someone who aready owns a house and you can convince them to build an ADU for you to rent, or even come to an aggreement to finance the ADU and later subdivide the lot so you can eventually own the property. Maybe you get a property that can be a business like a wedding venue or a museum or a hotel? Maybe you up and leave and move halfway across the country or halfway around the world. Maybe you sell everything, leave everything behind and go buy a small house in the country and drive a school bus or start an organic greenhouse or run a shop. Options exist especially at your income level. You just have to be willing to take a risk