The New Covenant is made with the House of Judah and the House of Israel only (Hebrews 8:8). Indeed, the New Covenant could not be made with any people who did not first have an Old Covenant.
The reference to Hebrews 8:8 is a part of a quote from Jeremiah 31:31-32 which reads, "Behold, the days are coming, says the LORD, when I will make a new covenant with the house of Israel and with the house of Judah - not according to the covenant that I made with their fathers in the day that I took them by the hand to lead them out of the land of Egypt, My covenant which they broke, though I was a husband to them, says the LORD." The statement is an assertion that both the people of the northern kingdom and the southern kingdom would receive a new covenant. However, there is nothing in this passage indicating that the covenant would be limited only to the descendants of Israel. It simply affirms that Israel would receive a new covenant.
Hosea prophesied of a day when a separate people would become God's people. "Then I will say to those who were not My people, 'You are My people!' And they shall say, 'You are my God!'" (Hosea 2:23). Paul uses this passage to prove that the Gentiles were able to obtain what the Israelites could not in Romans 9:25-29. He concludes with this statement, "What shall we say then? That Gentiles, who did not pursue righteousness, have attained to righteousness, even the righteousness of faith; but Israel, pursuing the law of righteousness, has not attained to the law of righteousness" (Romans 9:30-31).
Paul states in Ephesians, "Therefore remember that you, once Gentiles in the flesh -- who are called Uncircumcision by what is called the Circumcision made in the flesh by hands -- that at that time you were without Christ, being aliens from the commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world. But now in Christ Jesus you who once were far off have been brought near by the blood of Christ" (Ephesians 2:11-13). Notice the definition of a Gentile. A Gentile was not circumcised in the flesh, he was not a part of the Commonwealth of Isreal, and he was not a part of the covenants. Yet, all this lack of hope changed with Christ Jesus. Those once excluded have been invited to join. The writer of Hebrews tells us, "But we see Jesus, who was made a little lower than the angels, for the suffering of death crowned with glory and honor, that He, by the grace of God, might taste death for everyone" (Hebrews 2:9). Jesus' death was for everyone, no one was excluded. It was the purpose for which Jesus hung on the cross, as He predicted, "And I, if I am lifted up from the earth, will draw all peoples to Myself" (John 12:32). Thus Paul stated, "Therefore, as through one man's offense judgment came to all men, resulting in condemnation, even so through one Man's righteous act the free gift came to all men, resulting in justification of life" (Romans 5:18). That death was the foundation of the new covenant. "For this reason He is the Mediator of the new covenant, by means of death" (Hebrews 9:15). Or as Jesus stated while instituting the Lord's Supper, "This cup is the new covenant in My blood, which is shed for you" (Luke 22:20).
Hence, Jesus' death established a new covenant and that same death was done for everyone so that Jews and Gentiles would be invited into a relationship with God. This was predicted in Isaiah. In fact, God declared that it would have been too small of a task for Christ to simply save the Israelites. "And now the LORD says, Who formed Me from the womb to be His Servant, To bring Jacob back to Him, So that Israel is gathered to Him (For I shall be glorious in the eyes of the LORD, And My God shall be My strength), Indeed He says, 'It is too small a thing that You should be My Servant To raise up the tribes of Jacob, And to restore the preserved ones of Israel; I will also give You as a light to the Gentiles, That You should be My salvation to the ends of the earth.' " (Isaiah 49:5-6). Thus it was predicted, "Behold! My Servant whom I uphold, My Elect One in whom My soul delights! I have put My Spirit upon Him; He will bring forth justice to the Gentiles ... I, the LORD, have called You in righteousness, And will hold Your hand; I will keep You and give You as a covenant to the people, As a light to the Gentiles" (Isaiah 42:1). Notice that prophecy! Jesus would be a covenant and a light to the Gentiles.
And yes, a person can receive a new covenant without having an old covenant, just as I can receive a new car without ever owning a car prior to the gift.