Here's some anecdata: I bought an 800sf California condo in 1996. I used a stated income, aka liar's, loan because they're easier, especially if one is 100% commission, as I was. There were plenty of times when the mortgage payment ate up 50% or slightly more of my net income. I lived there comfortably, because I was good at managing the rest of the money. I continued to save, enjoy life, and even travel quite a bit, including ~ 20 states and two trips to Europe. I didn't have cable, I drove a used car, and took public transportation to work whenever possible, never ran up CC debt. Four years later, I sold it for more than twice what I paid for it.
My next place was much larger and cost about 7.5x my earnings. I was able to get another stated income loan, and I used the equity from the previous property to put 20% down. The larger place allowed me to have a roommate, which helped immensely. I paid $390k in 2001 and sold it in 2013 for $600k.
I sold it because I got married in late 2012 and our family's housing needs changed. We each sold our primary homes and paid cash for the next one. We got it on a short sale and paid $928k. I had just FIRE'd, so that amount was almost 10x our household earnings. Except we didn't need a loan. We knew the house was overbuilt for the neighborhood, but it allowed DH to walk to work, so we bought it, not expecting to see huge gains. To our surprise, it has nearly doubled in value.
Along the way, I/we bought three single family rental homes, all in the same resort community, which we still own. All three have lovely, low interest mortgages that we don't intend to pay off early.
That's how it happened for us in CA. I know Stated Income Loans no longer exist, but I made use of what was available to me at the time. I would say the keys were determination and willingness to make sacrifices to reach goals. I'd guess that's how a lot of people still do it.
