I'm probably the worst person to answer this question as I'm going through my own problems at the moment lol, but I will say what I think.
Of course it's possible but it requires both of you to be very mature minded and this is a lot of pressure for a young marriage. I'm assuming you're referring to the girl who is just 13? For legal reasons (depending on where you live) she will most likely need to be 16 at least which would make you about 21? This is more suitable as you would be mature enough to take on marriage but would she?
It honestly depends, if you know in your heart that you have the means to completely commit and to take care of your future wife at 21 years old then you should go for it. It's a big responsibility for a man to marry at a young age as he is the provider. So a women can marry without worry at 16 if her husband can provide but the husband has the duty to provide so if you know you can provide adequately, I think it's possible