I counter your argument to show the OP that it is possible. There is more than one way to do it, and this is just my experience. It's a long story, but maybe one the OP may benefit from:

I did not have family help, nor was I independently wealthy. I would say my income during the entire time was average, or maybe even below average. Without pulling out old receipts, I don't recall the total cost for my training, but I kept costs as low as possible by piecing my training together from different outfits with the lowest rates, and only committing for each phase of training when I had the money.

In high-school I bused tables, mowed lawns, worked at a hardware store, and pumped jet fuel at the local fixed based operator. I used the money I made to get my private license from a mom-and-pop place in my hometown. I went to college on an Air Force (AF) scholarship to avoid student loan debt. While the military covered tuition and paid a meager monthly stipend, I worked part-time jobs in order to eat and live. I did not do any flight training in college as I was expecting to enter AF undergraduate pilot training (UPT) after graduation. After experiencing the unexpected lesson of what "AF needs" really means, I was re-assigned from UPT to a non-flying billet as a logistics officer. At the time I was a single, new officer making about $40K the first year. To pay for the rest of my ratings, I kept my living expenses and costs as low as possible. I rented a house with several other officers, rarely went out to eat, and continued to drive my paid-for 12-year-old Honda. I focused intently on getting my ratings during nights and weekends when my day job did not interfere. I obtained my instrument and commercial at the base aero club. I took leave to attend a 10-day certified flight instructor (CFI) course out west. After obtaining the CFI license, that's when everything really started to pick up. When working a full-time job during the day, and instructing on nights and weekends, more money built up in my savings account for future ratings than any other time during the process. To the OP, getting your CFI is extremely important in the process. It allows one to build hours fast while adding more money into the savings account, all while keeping the income from the regular job flowing. At the time, the AF was offering an early out program to officers, so I left after two years of active-duty (AD) service and transferred to a part-time Guard unit. I worked part-time as an officer in a non-flying billet in the Guard and full-time as a CFI during the week. During that time I paid for my CFI-Instrument and multi-engine instructor ratings from the money I had saved from AD and from the money I was making as a CFI. In May of 2007 I accepted a job with a regional airline where they paid for the airline transport pilot (ATP) type rating several years later when it was required. Not counting the private license I obtained in high school, total time after graduating college to getting my first airline job at a regional was from Feb 2005 to May 2007, or a little under 2.5 years.

It may be tough in today's environment to obtain one's ATP without debt, but it is possible. In my case, the 1,500 hr requirement was not in place, but after obtaining the CFI license, a pilot's hours can grow very quickly. So instead of reaching one's objective in 2.5 years like I did, maybe it will take about 3.5 to 4 years to reach the ATP minimums in today's environment - but doing it debt-free is absolutely possible.