The law was given “because of transgressions” – Transgressions caused the law to be given. Transgression existed before the law was given, but we have this tendency to try to find ways to excuse our transgressions. Even now that we have the law, we still try to make out that certain things we’ve done weren’t really wrong, that some aspects of the law are a bit of a grey area, and in the circumstances you can’t blame us for doing what we did. And you can imagine that it would’ve been a lot easier to do that before the law was given, but the law shows our sin in black and white.
But the law didn’t come first. The promise God made to Abraham and his offspring wasn’t a backup plan that God came up with after it turned out we weren’t able to obey the law. We were never supposed to earn our inheritance from God by obeying the law. The promise came before we even knew we were breaking the law because the law hadn’t been given yet.
v20: “intermediary”/“mediator” – Mention of a mediator suggests you have two parties. One has offended the other, and the mediator facilitates discussions between the parties to work towards peace. So the mediator Paul is talking about has brought in God’s law, which clarifies what God has been offended by. Then the existence of a mediator suggests there’s God who’s the offended party and there’s another party that’s going to somehow pay for those offences so we can have peace with God, but in fact God himself is both the offended party and the one who has paid the price for our offences to make peace between him and us. The law wasn’t given so we’d know what we need to do to make peace with God. No one was ever going to fulfil the law “until the offspring should come” when God himself fulfilled the law for us in the perfect life of Jesus.