QUESTION: How can Jesus be the God of all people? He Himself said He was sent only to the lost sheep of Israel (Matt. 15:24).
ANSWER: This is a case of needing to distinguish God's program from His Person. And needing to distinguish the steps in His program from His ultimate goal.
His Program and His Person
As to God Himself, He is One God in three Persons. The Father is God, the Son is God, and the Holy Spirit is God, yet there is only one God. Each of the three Persons of the Trinity is fully God, and worthy of equal honour with the others, yet there is only one God. Each Person of the Trinity has a unique function and ministry, yet there is only one God.
We should not reject this truth simply because there is nothing we can see in nature that parallels it, or that can fully illustrate it. God is infinitely transcendent; He is utterly supreme and unique. Nothing, and no one else is like Him.
One of many attempts to illustrate the Trinity is a figure called the triquetra, seen above. It is one figure, with three distinct points, yet no point can exist without the others. They are all three interconnected and each is equal to the others.
That is helpful. But the triquetra fails to deal adequately with the uniqueness of each Person in the triune Godhead. As you see from the drawing, the points are all exactly the same, which is not true of the Persons of the Trinity. For example, Jesus Christ is both God and Man, but the Spirit of God is not a Man.
The difficulty of explaining these truths was not lost on the Bible's authors. John was a Jew who was taught there is only one true God (Deut. 6:4). Yet he wrote of Christ, whom he called "the Word" (cf. Jn. 1:14), and said, "In the beginning was the Word, and the Word was with God, and the Word was God" (Jn. 1:1). Or, as the Amplified Bible puts it: "In the beginning <before all time> was the Word (Christ), and the Word was with God, and the Word was God Himself."
Your problem of confusing God's program (what He does), with who He is, can be illustrated by something that happened to Queen Victoria, long ago. It was the custom of the queen to go for walks in ordinary clothes, with a faithful servant following some distance behind.
On one such occasion she came upon a flock of sheep, driven by a boy who rudely shouted, "Get out of the way, you stupid old woman!" The queen smiled, and said nothing. But when her servant passed by he informed the lad he'd been speaking to her Majesty the Queen. Totally unrepentant, the boy responded, "Well, she should dress like it!"
You seem to be asking that everything the Lord does must be clearly and evidently God-like, from your point of view. But would you have recognized Christ's deity if you were there to see Him hanging on a cross, or watched as they buried His lifeless body in a stone cold tomb? Not likely. Even His disciples didn't at first.
However, the Bible assures us of the deity of Christ over and over. He is "our great God and Saviour Jesus Christ" (Tit. 2:13). "In Him dwells all the fullness of the Godhead bodily" (Col. 2:9).
A number of times Christ is also said to be the Creator of all things (cf. Col. 1:16-17). The Lord Jesus Himself said, "All should honour the Son just as they honour the Father" (Jn. 5:23), and He took to Himself the "I AM" name of Jehovah God (Exod. 3:14) : "Most assuredly, I say to you, before Abraham was, I AM" (Jn. 8:58).
His Program and His Goal
Now, let's think about my second point. That we must distinguish the steps in God's program from His ultimate goal, and we must allow Him, as the sovereign Lord of all, to do what, in His infinite wisdom, He knows is the best way to reach that goal.
There is no doubt that God has favoured Israel in a unique way, above all the other nations on earth (Deut. 7:6). Four thousand years ago, He chose Abraham, and promised to make of his descendants a great nation, with a land of their own–a land that would be theirs in perpetuity (Gen. 12:2, 7; 13:15). Through Israel came the inspired Word of God (Rom. 3:1-2), and through them came Christ, the living Word (Rom. 9:5; cf. Matt. 1:1).
The Lord calls the nation "Israel My glory" (Isa. 46:13), something said of no other people. Of Israel it was said, "He who touches you touches the apple [pupil] of His [God's] eye" (Zech. 2:8)–meaning something especially valued by the Lord. And Israel is the special focus of the narrative in much of the Bible, from Genesis 11:27 (about Abraham's ancestry), all the way through to the early chapters of Acts.
In the Gospels, the Jews are still the focus on God's plan. Even in the promise of Jesus' birth to Joseph it is said, "He will save His people from their sins" (Matt. 1:21). That, of course, does not mean He was not going to save others too. But this was a message important to a believing Jew. (To say that the allies liberated Paris from the Nazis in the Second World War does not mean they did not also liberate France and other nations of Europe.)
As you point out, Christ's primary ministry, at first, was to "the house of Israel" (Matt. 15:24). And when Jesus sent to disciples out to minister, they too were sent only to the Jews (Matt. 10:5-6). Even the early Christians, after Pentecost, preached the gospel only to the Jews, at first (Acts 11:19).
However, the gospel of grace, salvation through the finished work of Christ, is "for the Jew first and also for the Greek [the Gentile]" (Rom. 1:16). "Jesus Christ–He is Lord of all" (Acts 10:36), not just Lord of the Jews.
When the Jews rejected and crucified their Messiah-King, the gospel message was extended to all nations. The disciples, whose ministry was restricted before, were then given a wider mission: "You shall be witnesses to Me...to the end of the earth" (Acts. 1:8) The Great Commission is to "make disciples of all the nations" (Matt. 28:18-20).
Why would the Lord favour one nation above all others as He did? I'm not sure of all the reasons–and He owes me no explanation for that. We do know that God blessed the nation of Israel and equipped them to be a witness for Him to the ancient world. "‘You are My witnesses,' says the LORD, ‘and My servant whom I have chosen'" (Isa. 43:10). However, through disobedience and unbelief, and habitual idolatry, Israel failed in this task.
Today, the church is the spiritual body of Christ (Eph. 1:22-23), made up of all nations treated on an equal basis (Gal. 3:26-28). It is a body, not with an earthly citizenship and kingdom, but a heavenly citizenship and kingdom (Phil. 3:20). And the church has taken up the work at which Israel failed: to witness to a dying world.
This wider work was part of God's plan from the beginning. Even in His covenant with Abraham we see it: "In you all the families of the earth shall be blessed" (Gen. 12:3). "The Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel to Abraham beforehand, saying, ‘In you all the nations shall be blessed'" (Gal. 3:8).
So, you see, though He had, and still has, special blessings in store for Israel as a nation, in fulfilment of His covenants, God had the salvation of all nations on His heart and in His sovereign plan, even then. But we must allow Him to work in His own way, while rejoicing in what He has done for us personally.