In New Age a person is working at their own divinity. In Buddhism it is an individual quest at being free from desire. And in Islam, the individual follows religious laws for the sake of paradise after death. The answer is yes. Not only can you connect with God, you also can know that you are fully accepted and loved by God.
Many religions place an individual on their own, striving for spiritual perfection.
Buddha, for example, never claimed sinlessness. Muhammad also admitted that he was in need of forgiveness. Instead, Jesus forgave people of their sin and he wants to forgive us of our sin also. God loves us but hates sin, and he has said that the consequence for sin is separation from knowing him. But God provided a way for us to be forgiven and know him.