I'll share an experience.
My (now) wife and I got pregnant in our senior year of college. That summer I had the good fortune to land my first software dev internship.
At the end of the summer, I was to be given an offer letter to come on as a full time employee after I finished school. I asked in that meeting if I could just continue to work and was told "uh yeah, that's fine I guess". Major victory for me at the time.
I did not share that I was soon to be a father until a few weeks before the baby was due. I was afraid that this situation would negatively color their perceptions of me and my work. But eventually the time came.
I pulled my tech lead aside and asked if I would be able to take a few days off for the birth. He said of course, but, at the time, I was still an hourly employee. My first son was born on Tuesday, I took unpaid time off for the rest of the week, then returned to the office less than a week after my son was born, the following Monday. I really had no other choice - I had been working for about 5 months at the time, and certainly couldn't afford to take any more hit to my paycheck.
About a month later, I asked HR if I had any kind of PTO accrued to take some time off for Christmas. This wound up being how I became a salaried employee - they felt bad that I didn't have PTO and said basically "oh, well, you're full time now anyway, we'll just convert you to salary."
I want to be clear that there was no malice or anything involved in any of these situations, and as a matter of fact, the company was very supportive and provided an absolutely wonderful first job. But still, there was just no procedure or infrastructure in place to support a 23 year old father. Everything that was done to help me through my internship and eventually full time employment was in some sense a just-in-time hack, done by kind people who knew and cared about me.
Had my career started at Accenture or some other gigantic corporate machine, I assume none of those things would have happened for me, even if the HR people were similarly benevolent. Even with all my good fortune, being a parent within the first few months of my professional career was difficult.
Nowadays, 6 weeks of parental leave seems to be pretty standard for professional jobs, and I imagine that benefit would extend even to someone at the entry level (maybe not an intern, but FTEs). But this is a pretty recent development. When my second child was born, I took a week off.
Later that year, the company implemented a single week of paternal leave for new parents , which you would just receive as an extra 5 days of PTO. A very kind and good technical manager, without my asking, went to bat for me and got me the week of PTO refunded, effectively grandfathering me into the new benefit. No one had to do that for me, it didn't even occur to me to ask - but I have remembered that act of care from him for a long time.
So, all told, I had a pretty good level of company support as a young parent. But it's quite easy for me to imagine that any of these strokes of fortune wouldn't have occurred for many others in similar situations.