My own advice is not to marry her as in so many similar cases, marriage takes place and few years down the line, the break up and the woman takes the children and makes them Christian and the Muslim man ends up seeing his Muslim children turn into Christianity!
My advice would be that you go to that masjid and tell them about your situation and you will find in sha Allah a Muslim woman who would be willing to marry you. Meanwhile, you should fast until Allah makes a way out for you!
If this doesn’t appeal to you, you can marry this woman only in the Islamic way which requires her guardian’s approval and the presence of two male Muslims.
He tells you: I give you my daughter in marriage and you say I accept her marriage and that is it! You of course assign a dowry for her and give it to her!