Adam knew God, he heard the prophecy of the Messiah to come who would redeem him from his sins, believed it, therefore he was a true believer, which is a Christian.
The new Testament was intentionally written in Greek and the Greek rendering of Messiah is Christ. Adam and all after him who truly loved God were given the gospel. The gospel is simply that God would become a man and die for our sins and be resurrected to life again, and that all who come to Him for forgiveness will be saved. Adam knew the Messiah was coming one day and believed. Or, in the Greek, Adam knew that Christ was coming one day and believed.
True believers, Jew and Gentile, who believed on Messiah, were Christians…from Adam, on up to this day.
David was a Christian. Moses was a Christian, Samson was a Christian, Nebuchadnezzar was a Christian. They all believed Messiah was coming to save them from their sins. How simple is the gospel!