Is it permissible to intervene to find a family to sponsor a child born out of wedlock, knowing that the mother will not be able to see the child in the future, and what is the ruling of Islamic law on this type of sponsorship and its conditions?

The woman must offer sincere repentance, express remorse, and seek forgiveness. If she needs to place her child with caregivers, he must not be attributed to them; rather, he should be attributed to his mother or given names such as "Ibn Abdullah" (son of Abdullah). It is not permissible to give the child to people who stipulate that his mother should not be known, as this constitutes severing ties of kinship and disobedience. The solution is to search for a family that does not stipulate attributing him to them, nor severing his ties with his mother, nor refusing to return him to her if she requests him.