It may be normal, but is it productive? What will you do? Stop loving your child, punish the mother? You may be better off not knowing the answer and being OK with that.
As for your partner, the State saying you cannot verify whether they have been cheating to you or not is a huge step in the wrong direction. because you can easily check it anyway, but you can not use this knowledge to assert your rights.
They are not your child. They are someone else's child. Maybe you keep loving them the same. Maybe you don't.
> punish the mother?
That would be barbaric. You wish your former partner all the best, and you part ways. Or you don't. But if people can divorce over "nothing" then that level of dishonesty certainly qualifies for one.
Not your child.