Our generation gets 25-year mortgages, and very little help from inflation.
As someone born in the 1980s in the USA, I don't think this is true. I believe that the 30 year mortgage has been the standard here since sometime in the mid 20th century.
Another thing to keep in mind is that there far fewer homes and people made a lot less money.
You don't need a new house for every young person.
You can reuse houses across generations. 100, 200 and even 500 year old houses are not uncommon in Europe for example, if you build them properly (and not the el-cheapo wood US construction). They're not any kind of ruin either, but highly coveted city and rural real estate.
Plus, there's an existing pool of a hundred million houses or close, so you wouldn't have to worry about getting them a house either.
Lastly, debt means money owed. A government can also money it actually has (e.g. form taxation, dropping military expenses and so on). Presumably there's still that.
Not to mention that the government could still ask for payments for the houses, but for a much smaller interest, and without expecting a profit, allowing people to repay them much earlier.
This is not some communism plot, places from England to Singapore, most of EU and beyond have done public housing in different degrees. England's public housing plan, for example, implemented for the most part of the 20th century, turned it from a country of extreme poverty slums (think L.A.'s seedier districts but in Dicken's London and Manchester and elsewhere) into an acceptable middle class (they'd call it "working class") existence.
The only way a young person could be given a house without owing any debt would be if someone else bought it for them or if the government paid workers to build houses for everyone. However, if the government paid people to build houses without any payments in return the government would be collected the debt which it would then hold. This doesnt reduce any debt globally it just transfers it.
Maybe you could argue it is better for the debt to be on government than individuals but that doesnt address how no debt is good. No debt would just mean zero houses.