Not possible. The minor is not emancipated. her father lives out of state and her mother is hospitalized long-term in another county.
How do you know it's not possible?
It is most certainly possible for a father in a different state to give permission for a child to marry. And it's absolutely possible for a mother who is hospitalized in a different county to give permission for the marriage.
Or, there may be a court-appointed guardian who could give permission.
The court has procedures to follow before they will grant a marriage license. She would have been required to present her ID showing age -and since she's under 18, the court would have needed permission of the parents.
If you have reason to believe that they made a mistake, you're free to call the court clerk, but I doubt if they'll even talk to you because it doesn't concern you. Or, you could probably call CPS if you think that a child is marrying without the parent's permission.
I suspect that you're in for a rude awakening.