I think it's really great that, for the sake of your child to live in a good home, you are willing to help your ex buy her house after your separation. Others are right to say it's not a gift though. It's part of the separation agreement, in lieu of her getting half the furniture or something, and that way should the agreement end up back in court, you can show that you have already paid her a significant amount and she doesn't need more. Unfortunately, there are many many ways for her to take advantage of this, and it's not going to be easy for you to make it iron clad.
As others have stated, you cannot pay CS 'ahead' in a lump sum like this. Paying SS in a lump sum is also ill-advised. Should she manage her money poorly and lose the house, she can always take you back to court to get that monthly CS amount out of you. Heck, she could turn around and SELL the house a month after she closes on it, get all your money back in cash, and blow it all on herself. I'm really not sure what to suggest so that your child is guaranteed to benefit from it, as you are no doubt hoping.
But unlike asking a lawyer for advice, there are a lot of people here to brainstorm more ideas for you, and it's free!