This is a teaching from the first day of Christ's visit with the Nephites. It is a quote from Christ.
The time frame in which the Gentiles were to have "belief in [Christ,]" and merit a special blessing as a result, was the time immediately following the Judean ministry. The Gospel would be taken to the Gentiles and they would believe. The Jews were going to reject Him and oppose His faith, the Gentiles would welcome it and have belief.
Now the words Christ spoke and Nephi's record preserved were from "the Father." Christ's explanation of these prophecies originate with His Father.
Gentiles will believe. Moreover, the "house of Israel" will not believe in Him. The result of that acceptance and rejection is the juxtaposition of the roles of Gentiles and Israel.
Whereas, the Gospel came to the Jews first, and by the Jews it was transmitted to the Gentiles, later the opposite will occur. The pattern will reverse. It will go from the last back to the first. (It is an historic chiasm.)
Accordingly, the Gentiles will be the ones to whom the restoration of the "fullness" will come in the latter day. The reward for earlier faithfulness is later recognition and reward.
Now, it should take no amount of brilliant insight to realize that the restoration involved Joseph Smith. A man of English descent. May have some Israelite blood in him from the earlier disaporia of the Lost Ten Tribes, but he is nevertheless the one through whom the restoration was brought. He is necessarily identified as a "Gentile" in this prophecy by Christ, given by the Father. If Joseph Smith is NOT a Gentile, then the whole promise of the Father and word of the Son is defeated. Therefore, you may know for a surety that the Gentiles are not those nasty non-members. It is US. WE are the Gentiles who receive the first offer in the last offering.
So it was that the Father determined and Christ taught that the Gentiles would be the ones to whom the Gospel message would first come in our day. Now we have it. (Or had it anyway.)
This movement from Israel to Gentile and from Gentile to Israel is evening the playing field. This is balancing out the record of history. It is not that one is more favored than another. Rather it is that each one will have a suitable turn and opportunity to receive what the Lord offers. In the end, no people will be able to say the opportunities were unfair, unequal, or more challenging for one than for another. [I leave it to you to determine why that is so when lives come and go across generations and one dispensation may include different people than another. It raises the question as to how certain we should be about some of our premises. That, however, is too far afield at the moment. And it may not matter anyway. Today is the day of salvation, not yesterday or tomorrow. So we should confine ourselves to solving the problem we face at the moment.]
The promise is that the "fullness of these things" will come to the Gentiles. What things? What does it mean that the "fullness" will be coming to the Gentiles? Have the Gentiles in fact received it?
If we received it, what have we done with it? Do we still have it? If not, how do I know that? What will happen if we have not retained that fullness?
Fortunately for us, Christ will answer all those questions as He moves along in the message He delivers here.