Yes, children who are born into these problems will find it especially difficult to get themselves out of poverty.
Yes, i f you show me a single parent on minimum wage supporting multiple kids and family members, it seems guaranteed that they'll be in poverty.
However, the cause of their poverty isn't that they aren't making enough money. It's that their expense level is too high relative to their income.
Addressing poverty requires reducing the level of expenses relative to earnings. Let's start seeing both sides of that equation addressed.