Why do you aspire to go to university, OP?
I did as an escape, at first. I had universities sending me their brochures back in the 90s when I was 10 and they still sent out paper brochures. There was a clear difference between those where the expectation even before finishing school was to work for income as much as possible, that for many is a normal family, and those where university is normal, living in areas where teenagers can easily access university libraries. It then became the only way not only to get out, but to continue with my interests.
People discussing things in a positive light or saying they are proud of what they've done doesn't mean they are bragging. For it to be bragging, it needs to be excessively boastful. People can just be happy with things they worked towards or statements of fact, as all the examples I'm seeing have been.
I'm not the first in my family - my father went, my grandfathers both went, they benefitted from the US's GI bill and similar that more actively supported them in ways those trying now will really struggle to get. I'm the only one of my siblings to go - I'm the only one without legal/drug trouble, I'm the first woman in my family, to my knowledge, and I got into university based on an email conversation I had with a head of department on his niche - they bent the usual admission rules to admit me based on my interest even though I didn't mean the qualification requirement because, as they said, the way I wrote about it was enough evidence. I'm not sure how many unis would allow that these days.
I said in my op if you’re from an actual dysfunctional family like heroin addicts or alcoholics of course it’s an achievement.
My parents were both addicts for my entire childhood, even the university educated one. They literally got together over sharing drugs. My mother lost custody due to her violence. Dysfunctional would be an understatement.
It was still fairly for me to imagine and work towards university as a way out compared to many of my peers who had no experience of that. I figured if they could do it, I could figure it out. That wasn't true of many I knew who didn't have that around them, even without the drug addict and violence in the family.
Even with more kids going to uni, I think the divide is only getting bigger. I was a governor at local secondary and even with staff very focused on promoting universities, the benefits are becoming less visible as many with degrees are working jobs with those without. I've met more than a few kids who only want to go to uni through a degree apprenticeship or similar route where they get paid because even with so much trying to make it normal, normal in many places is still needing to pay the bills that are only growing. Potentially putting that off/making it much more limited for 3-4 years is not something every young adult can feel is realistic or safe to do.
Lots of personal attacks because I was a young mum but I’m going to uni once my kids are a little older
I was a young mum, had one as a teen, had two more while at university. I have fond memories of writings and finishing my dissertation with a baby sleeping on me. You can likely do it, though to get through the difficulties, a strong reason why is often vital, as it acceptance that it doesn't automatically lead to that better job. There is a reason some industries brought requiring removing dates on 'blind' CVs - there is a hiring bias about those gaps and age.