If you really liked someone why hesitate in going for a relationship even if they already have a child? Well I guess it would be a shock since you didn't expect them to already have a child and being a single parent at that.
Adult relationships are not simple, you either pursue the relationship, faults and all (unless those faults are them being abusive, has a history of cheating, or whatnot), or not at all
Edit: adding this because I read something stupid here in the comments.
Finding out that the person you want to have a relationship with already had a child is not a deal breaker. If you love the person, you have to accept their past and not just their present. You are no longer a child that should think that person is no longer a romantic interest just because she had a child with a different man long before you came into the picture.
You do not necessarily need to be that child's father anyway. You can be their father-figure, but unless the child chooses to, you do not necessarily have to be their father.