Answer: Circumcision is not just another commandment. It is the everlasting sign of G-d's covenant with the Jewish people. In fact the Hebrew word used to describe the occasion of circumcision is not "Milah" which means circumcision but rather "Brit" which means covenant. It affects an eternal bond between the Jew and his creator.
A covenant made by mortals, though they may be the best of friends, is always subject to change. G-d, however, does not change. When He makes a covenant it is truly everlasting and eternal. Our relationship to G-d is not based on a mutual intellectual decision and choice where we concluded that we are good for each other. Rather it is a suprarational choice made by G-d alone to have an inherent, intrinsic and eternal bond with His people. It is unconditional and can never be broken by any form of rational logic.
A child at 8 days old has not yet achieved anything, is definitely incapable of making any rational choice and could never take the initiative to connect to his creator. But his creator wants to connect to him. This first mitzvah expresses our unconditional connection to G-d as a nation - one that comes only from G-d's eagerness. It is a union coming from the creator alone, independent of any achievements and qualities, but rather a bond with the mere existence of our souls.
For this reason a Bris is held specifically on the 8th day. The number 7 represents the cycle of life, the order of nature - 7 days of the week, 7 days of creation. The number 8 represents that which transcends the natural order of things. It is through the act of a bris that one attains a union that surpasses nature by embedding in the body an everlasting bond that surpasses all rationale. A union based only on the fact that the child is a Jew. This is a bond that can never be terminated.