I think God putting Adam into a “deep sleep” was the cultural way of talking about God giving him a vision imparting great spiritual truth. (This comes out in comparative ANE lit studies.) The word translated “rib” is an unfortunate tradition in English, and the Hebrew word is usually used for a side or a half. So God was showing Adam that Eve was his “other half,” the designated counterpart provided him by God (also a theme in ANE lit), and that together they formed a complete whole, “the two become one.”