you only need a comparatively (compared to the overall cost of the property, even if in cash it's not a small amount) deposit. The average house price in the UK is £268,421, which means approx (I know not exactly) 50% of houses are under that.
FTB are going to be more likely to buy the houses at the lower end of the scale. 5% of £200,000 is £10,000. If there are two of you, that's just over 1 year of saving £4k each in a HTB ISA and you then get a free £1250 each, deposit sorted. Of course you might be buying alone, or want/need a 10% or higher deposit but if you're working full time from age 18 or 21 then saving a few K a year would get you that amount by your mid twenties or early 30s, particularly when those are also the years you'd hope you'd be progressing in your career a bit. And of course (although SE focussed 'naice area' MN posters refuse to accept that anyone would want to live in them) many properties are much cheaper again.
Obviously not everyone can afford to save due to various circumstances, and some people don't start saving until later, but it's hardly a completely impossible ask that's out of reach for everyone. And that's not even going into inheritances, bank of mum and dad, etc.
You may as well say 'Where do people find the money to rent?' People have to live somewhere, it's either rent or buy. Once you've got the deposit a mortgage can often be cheaper than per month than renting.