In stereotypical Jewish fashion, allow me please to answer your question through asking yet another question.
Why can't the brit (circumcision) wait until the child grows older? Wouldn't it be that much greater if a mature person, using his own intelligence, would choose to make the big decision himself?
But that's the beauty of a brit. We are born Jews. It is not a project we rationally decide to undertake. Our covenant with G‑d is super-rational. It does not go away in moments when our minds tell us otherwise. We do not always comprehend the reasons behind the mitzvot.
According to Kabbala, the number seven represents nature and that which is finite. Seven days in the week, seven days of creation, and seven human faculties.
Eight represents the super-rational and the infinite. The miraculous as opposed to natural. Belief as opposed to comprehension.
And so, a baby is given is brit on the eighth day. He is entering a religion founded upon faith, whose survival is miraculous, and whose potential in the world is infinite.
Rabbi Yisroel Cotlar