Moses wrote the Pentateuch. His parents were from the tribe of Levi.
Various Hebrew authors wrote the Psalms, and various Hebrew prophets God sent to the Hebrew people wrote their prophecies. From Genesis to Malachi record the beginning of the Hebrew people up to four hundred years before Israel's Messiah arrived to and for the Hebrew people. Jesus Christ/Messiah was prophesied many times by Hebrews in their various capacities as servants of God. The whole bible from Genesis to Malachi records the history, culture, religion, and other particulars of the Hebrew people and God's covenants with this people to protect them, teach them, and to provide to them. Jesus Christ was prophesied to and for the Hebrew people as per covenant and prophecy. When Jesus arrived and began His Ministry to His people the purpose of His coming was to be the basis for God to keep His promises to deliver this people from their enemies, give them their own land, and provide the means of eternal salvation to this people.
The four gospels were written so that the Hebrew people have a history of many important parts of Messiah's life and Ministry to this people. Jesus wasn't sent to non-Hebrew Gentiles. He was sent to the lost sheep of the House of Israel. In keeping with the Law, especially the Ceremonial Law, Jesus Christ fulfilled the function of the animal sacrifice which under the Law the sins of the people of Israel were covered and then removed by Israel's Messiah, Deliverer, Savior, and King.