While we may not be able to fulfill God's law on our own, Jesus Christ fulfilled God's law and offered his righteousness (and himself) on behalf of us. This is part of the concept of "justification", which is basically being able to stand right before God. Since none of us can accomplish God's law on our own, justification is from faith in Jesus Christ (because Jesus provided the righteousness of God). But justification by faith isn't really a new concept.
A long time ago, there was a guy named Abraham, who is considered to be a father of some prominent world religions (including Christianity). Abraham was the one who got a lot of promises from God and believed God. His story can be found in Genesis. But notice that when Abraham believed God, "it was accounted to him for righteousness" (4:3). In other words, Abraham was justified by his faith.
Paul even talks about how if Abraham was justified by works, Abraham could boast about something, but that boasting is "not before God" (4:2). From these two information, the justification happens because of faith rather than works. Though keep in mind that the justification is regarding from God.