When it comes to Faith vs. Law, Paul picks out the perfect example in Abraham. We’re talking about the founding patriarch of the nation of Israel. So he’s universally respected by the Jews (and thus the Judaizers). But he predates the Law by hundreds of years. How then can the Law be the only way to salvation?
“Scripture foresaw that God would justify the Gentiles by faith, and announced the gospel in advance to Abraham: ‘All nations will be blessed through you.'”
Abraham was just as fallible as the next guy, making big mistakes along the way, but believing in the Lord’s promise and working out his Faith which was credited to him as righteousness.
In contrast, the Law cannot save, it can only point out our sin and condemn us for it. If nobody is sinless, then the law allows for no salvation. It is only through atonement that we are saved and when Christ gave himself up on the cross, he provided for us the perfect atonement for our sins. The law certainly does it’s part in pointing us to the feet of the cross, but it cannot save us by itself.
The end of chapter 3 reads almost like a civil rights speech. There is no Jew or Greek or slave or free, we are all one in Jesus. A fitting retort to those who wished to divide and create a sort of caste system in the early church.