Don't give up yet! It does take time. Some women feel the connection when they make one good friend in the chapter. Some women feel the connection when they have a specific role to play such as a committee membership. Others find the connection through being there for a sister who is hurting.
It comes along in different ways for different women. But definitely do not give up a lifetime of sorority membership after only a week! It could even take a few months to really feel connected, but it will happen. Just give it time.