Not as "the Ten Commandments", no, but if you read the Hebrew scriptures from creation up to the time of Moses, you will discover the principles of all those laws were known to all of God's people in those earlier times.
Murder, for example - read how God challenged Cain about the sin of murdering his brother, which he was nurturing in his heart (Genesis 4:6-7 & to Noah and all his descendants in 9:1-12).
Stealing, lying, adultery etc was also known by God-fearing people to be against His ways though you will not find a legal statement about that pre-Moses. (Job 23:12, 31:1 & 9-40 for all the Ten Commandment principles, including how polytheism was also known to be massively against the only true God. Job was reckoned to have lived long before Moses.)
So, the principles of all ten commands existed long before Moses, but they were never set down in stone until God's finger carved the words out on tablets of stone.