Can a man sign over his rights to a child even if there is not another man to adopt the child?

The short answer is no. Hopefully you and your spouse can work through the betrayal that may well be arising due to his poor choice, but state law does not permit a biological father to simply call for a mulligan and act as though that night never happened if the night produces a child. Until the test comes back, he is simply alleged to be the father. If paternity is established, he can not be forced to be a loving father. Nor can he be legally denied the opportunity to be active in the life of a child if he desires to be a loving father going forward. A spouse's betrayal can indeed rock a marriage, but it is up to the two spouses whether it will destroy their union. Some can not get past it, some can with outside counseling assistance, and some can focus on moving forward working it out between the couple. As for your child you brought into the world together, how she will accept and adjust to learning of a half-sibling, if indeed this becomes the situation, will largely be dependent on how the parents react initially, how the news is presented to her, and what level of involvement the father takes in the life of both of the children. There is no reason the news of a half-sibling should be treated as automatically devastating to your existing child.