Do you consider "God's law" to be the same as the law given to the Israelites alone through Moses?
(sorry for the loaded question, I want to be specific)
Indeed. In Deuteronomy 5:31-33, Moses wrote down everything that God spoke to him without departing from it, which is why the Law of Moses is called the Law of God in verses like Nehemiah 8:1-8, Ezra 7:6-12, and Luke 2:22-23.
If so, what was the law before the law? (given to the Israelites alone through Moses)
The law before the Exodus.
God’s character traits are eternal, so there has always existed a way to be a doer of them regardless of when God gave instructions to for how to do that to Abraham, Moses, or someone else.
In Matthew 4:15-23, Jesus began his ministry with the Gospel message to repent for the Kingdom of God is at hand, which was a light to the Gentiles, and the Law of Moses was how his audience knew what sin is (Romans 3:20), so repenting from our disobedience to it is a central part of the Gospel of the Kingdom, which is in accordance with Jesus being sent as the promised seed to bless us by turning us from our wickedness (Acts 3:25-26), which is the Gospel that was made known in advance to Abraham in accordance with the promise (Galatians 3:8), which he spread to those in Haran in accordance with the promise (Genesis 12:1-5).
The Hebrew “yada” refers to intimate relationships/knowledge gained by experience such as with Genesis 4:1 where Adam knew (yada) Eve, she conceived, and gave birth to Cain. God’s way is the way to walk with and know (yada) Him and Jesus by embodying His likeness through experiencing being a doer His character traits, which is the way back to the Tree of Life (John 17:3). For example, in Genesis 18:19, God knew (yada) Abraham that he would teach his children and those of his household to walk in His way by being doers of righteousness and justice that the Lord might bring to him all that He has promised. In Genesis 26:4-5, God will multiply Abraham’s children as the stars in the heavens, to his children He will give all of these lands, and through his children all of the nations of the earth shall be blessed because he heard God’s voice and guarded His charge, commandments, statues, and laws. In Deuteronomy 30:16, if the children of Abraham will love God with all of their hearts by walking in His way in obedience to His commandments , statues, and laws, then they will live and multiply and God will bless them in the land that they go to possess. So the promise was made to Abraham and brought about because he walked in God’s way in obedience to His law, he taught his children and those of his household to do that in accordance with spreading the Gospel of the Kingdom that was made known in advance to him, and because they did that in obedience to the Law of Moses.
In Exodus 33:13, Moses wanted God to be gracious to him by teaching him to walk in His way that he and Israel might know (yada) Him, and in Matthew 7:23, Jesus said that he would tell those who are workers of lawlessness to depart from him because he never knew them, so the goal of the Law of Moses is to graciously teach us how to have an intimate relationship with God and Jesus, which is the content of the gift of eternal life. So both Abraham and Moses spread the Gospel of the Kingdom by turning people from their wickedness and by teaching them to walk in God’s way in obedience to His law.
Note: Israel did not keep the Sabbath before it was given in Exodus chapter 16.
There are many examples of God’s laws being in place prior to Sinai, so Sinai being the first record of a law being given does not imply that it is the first time that it was given. For example, in Genesis 4:7, God told Cain that sin was crouching at the door and that he must master it, which implies that he already knew what sin is and had already been given laws in that regard. In Genesis 5:24, Enoch walked in God’s way. In Genesis 6:8-9, Noah found grace in the eyes of God, he was a righteous man, he walked with God, so God was gracious to him by teaching him to walk in His way and he was righteous because he obeyed through faith. In Genesis 7:2, Noah was told what to do with clean and unclean animals without being told how to tell the difference, and in 8:20, he knew to offer a clean animal. Again with Genesis 26:5. In Genesis 38:9, Joseph knew that it was a sin to commit adultery.