The lack of a child’s birth certificate cannot in any way be the basis for refusing to admit a child to a school in Poland. Compulsory education covers all children aged 7 to 18 residing in the territory of the Republic of Poland (pursuant to Article 35 (2) of the Education Law and Article 28 (1) (a) of the Convention on the Rights of the Child), regardless of their citizenship or legality of stay. The child not only has the right but also the duty to learn. The school or kindergarten is obliged to accept the child, and the solution of formal issues – regarding the required recruitment documents – is a problem that must be solved by the school or kindergarten itself.
In case of refusal to admit a child, read: https://ukraina.interwencjaprawna.pl/what-to-do-if-the-school-does-not-want-to-accept-the-child-to-attend-to-school/