Is it sad that this feels like a trick question?
Ha! That was my first thought, "The average age that people are debt free in America ... is never?" There is birth, but assuming the target audience is adults, specifically those that have gone into debt, a fair number are always in some sort of debt. House, car, credit cards, school loans, general loans, lines of credit, store credit, etc.
Before we bought a home we carried a credit card balance longer than a month twice in 13 years. But we are outliers as we have purchased every vehicle with cash and consciously made decisions not to be in debt. Which hasn't always been easy as I have never earned over $50k and we have 6 children. But almost everyone we know (except my wife's parents and her siblings) live in a debt cycle, and not just mortgages. Some of it is manageable, others not. Some of it is smart (right sized housing that fits employment) and some isn't (credit card debt for non-essential consumables and entertainment). Alas a lot of people take debt with them to their grave and it goes against their estate. So I guess at the average age of death ~ 77 a large segment of people have some debt until the day they die. That number of people is much higher than the "completely debt free" crowd.
So the question is a trick question in that what are your baselines? How do you factor in those who have NEVER been in debt?--give them age 0?
A better question would be, "What is the MEDIAN age the average ADULT American is debt free?"
Answer: About 77 years (i.e. average age of death).
But that isn't the same thing as liquid. Of those individuals how many are liquid at death--how many who have assets that satisfy their debts? That is a good google question. And complicated when looking at a living individual and their debt load--it isn't dissimilar to a company. If my personal Balance Sheet is + $100,000 but $300,000 of that is tied up in my house that isn't really a liquid asset. So if I have $50,000 in liquid assets (cash, short term investments) but ($250,000) of debt that could be a problem if the debt is short term debt as the house asset isn't easily tapped without selling. Which poses a problem, i.e. you need a place to live.
This is why we have chosen to live debt free as much as possible. We aren't financially stupid but debt has risks. This year
we elected for long term debt (mortgage) as at this point in our life/my employment the benefit over renting for us is worth the risk in our assessment.
Obviously this forum is chalk full of 6 figure financial geniuses with financial savvy so my comments are rudimentary and approach far too conservative. But I think the takeaway on a forum like this is the typical poster in a thread like this is a couple sigmas above the average American when it comes to understanding finances and debt. The fact the posters here are thinking and engaging in financial questions shows a level of awareness more so than many Americans. It is difficult to say what is right/wrong for every individual as living circumstances are so vast but the starting point is putting the thinking cap on, become familiar with basic concepts, and being deliberate in your finances. For those in their 20s and 30s that would put you in the top 10% of your age bracket as many at that age don't put much thought into such things.