I'm in my late 30s. Single mother to two children, though one is a mid-teen by now, but the other still needs wraparound childcare.
It's entirely doable. I did it after my ex husband and I split up. I have no financial backing from parents (I am non-contact with one and very low contact with the other). I started again with nothing and having left an awful lot of stuff in the marital home for the sake of a quick divorce.
The first thing I did was to push for promotion at work to get more money - something that was granted after 2 years of very hard graft.
I rented a cheap house in an undesirable area from a landlord who had no real interest in maintaining the property bar the bare basics. It enabled me to save, and I was brutal: £300pcm minimum went into a savings pot - more if I was able to work more days or make significant savings elsewhere.
I haven't been on holiday for about 5 years and outings with the kids are still very much cheap or free things to do, such as walking in the woods, natural crafts, the occasioanl trip swimming or ice skating - never anything big. My car is almost 20 years old and looks it.
A year ago I managed to buy a cheap terraced house, having saved a mere £18,000. Again, it's in an undesirable area, not very pretty on the outside, but, being ex-council stock, it's spacious and really well-built in that I don't hear my neighbours at all.
I learned enough DIY to get by - the teen and I painted all the rooms, I learned how to carpet a room and thus saved enormously on labour costs carpeting two rooms on my own. I bought flat pack furniture and built it myself, or got charity shop furniture. I fixed my own curtain rails. I changed door handles from ugly plastic shite to more modern ones, found two local roofers just starting out to fix things on my roof and clear the gutters cheaply but well. I sealed any gaps to save money and heat over the winter. I did some basic gardening to make both the front and back visually more attractive. I used end-of-season beachware, such as beach mats, to decorate my bathroom. Over the summer I will be tiling the bathroom, re-glazing the tub and getting a shower installed.
Every month I do one or two jobs on the house to make it slightly more attractive. It's a work in progress and if you want your own place and don't have financial backing then it's unlikely you'll land your dream home, but you can make any house into a dream home with just a little bit of work.