Part of Biblical prophecy is "typology." A typology is basically a picture of something or someone in the Old Testament that foreshadows something or someone in the New Testament.
Solomon was the son of David. His is called by a few different names in Scripture. When he was born, the Lord loved him and sent His prophet Nathan to tell David that the Lord wanted him to name his son, "Jedidiah," which means "beloved of the Lord." When he was made king, God named him Solomon.
This reminds me of the Lord's voice speaking out of Heaven as Jesus rises up from His baptism, "This is My beloved Son, in whom I am well pleased." (Matthew 3:17) Also, God's messenger angel tells Joseph that Mary would have a son and they were to name Him Jesus.
Solomon is a picture of the Messiah, specifically as Jesus Christ will reign in the Millennial Reign. Here are some of the ways that he prefigures Jesus reigning here on Earth for that thousand years:
His reign begins with judgment: Solomon's brother, Adonijah, sought to take advantage of King David's poor health and attempted to snatch the kingship that was promised to Solomon. The prophet Nathan finds out and warns Bathsheba. Together they both warn David.
David quickly orders Solomon crowned king. Nathan, and one of David's mighty men, Benaiah, lead Solomon to Gihon where Nathan anoints David. Incredibly in recent years an Israeli archeologist discovered the King Priest Melchizedek's altar at the same place!
Adonijah seeks mercy, and Solomon pardons him. But after David's death, Adonijah tries to become king and Solomon sentences the would be usurper to death.
Jesus will begin His reign here on earth with judgment. Matthew 25: 31-33, 41 describes that judgment:
"But when the Son of Man comes in His glory, and all the angels with Him, then He will sit on His glorious throne. All the nations will be gathered before Him; and He will separate them from one another, as the shepherd separates the sheep from the goats; and He will put the sheep on His right; and the goats on His left...then He will say to those on His left, 'Depart from Me accursed ones, into the eternal fire which has been prepared for the devil and his angels."
Jesus is described as "having become a high priest forever according to the order of Melchizedek.
In Solomon the wisdom of God is manifested.
After David's death, Solomon, described in 1 Kings as a man who "loved the Lord, walking in the statutes of his father David," sacrificed a thousand burnt offerings. That night, the LORD appeared to Solomon and told him to ask whatever he wanted from God. Solomon asked for wisdom.
Pleased with Solomon's request, the Lord gave him such wisdom and discernment that no other human ever had before or ever would. Indeed Solomon's wisdom is noted over and over in the Bible.
We see in the New Testament, Jesus is the wisdom of God. (1 Corinthians 1:30). In Jesus "all the treasures of wisdom and knowledge are hidden.
Before he died, King David told Solomon about God's plan for his kingship. Because David had shed so much blood, he could not build the temple, but his son would. In addition to building God's temple, God promised that Solomon would rule over Israel in complete peace. There would be no war in his reign! (1 Chronicles 6-9)
Revelation 20 details the facts of the 1,000 year reign of Jesus Christ. Satan will be bound. Those believers who survive the Tribulation will go into the thousand year reign of Jesus and will have children. In the Old Testament, we're given a picture of peace and blessings in the Kingdom. There will be peace among the animals. Weapons of war will become farm tools. "Nation will not lift up sword against nation, and never again will they learn war."(Isaiah 2:4b)
Ezekiel 40-48 describe the Millennial temple. The world has seen nothing like it! The glory will return!