Getting married at a young age doesn't lead to poverty. Getting pregnant and having to raise a kid at a young age leads you to poverty especially if you have too many of them or the parents themselves doesn't have the financial capacity to raise a kid properly. I know of people who got married early and are still making profit.
I dont think so because if you can manage your expenses and earnings, you will never face poverty. It is right that if your income is limited and your family is large then you will not be able to fulfill all their needs and dreams. As your family gets longer your daily expenses will increase and for that you will need more money to overcome and if you dont then you can face financial problems.