Was the God who gave the Law at Sinai the same God who later gave Paul the doctrines of grace?
Yes. The God who gave Moses the Law at Mount Sinai is the same God who, about 1,500 years later, gave Paul the doctrines of grace. Scripture presents God as unchanging; He simply dealt with a different individual, Paul, and sent the message to Gentiles and Jews.
Les explains that God did much the same thing with Moses at Mount Sinai: God gave Moses the Law, and Moses took it down to Israel, though the Law affected the whole human race. Then, about 1,500 years later, God had not changed; He is still the same and never changes. The same God now dealt with a different individual, Paul, giving him the doctrines of grace embedded in what Paul calls the Mysteries. Paul was not instructed to take it down to the nation of Israel, but to take it far hence to the Gentiles, and of course the Jews. Les emphasizes that all of it is God's Word, and that Paul is the Apostle of the Gentiles, referencing Romans 11:13.