If Jesus wanted to save non-Hebrew Gentiles, He would have prayed for them right before going to the cross:
9 I pray for them: I pray not for the world, but for them which thou hast given me; for they are thine. John 17:8–9.
In John 17 above Jesus as High Priest does two things which the high priest does always under the Law, that is, pray for the people of God in covenant, and offer sacrifices for the people of God in covenant. Jesus, as High Priest, does neither in John 17 in a prayer Martin Luther calls the "Holy of Holies" Prayer.
If you read John 17 Jesus makes a distinction between "the world" and "Them" (the children of Israel, including the 12 disciples.
From the cross Jesus completes His Ministry as High Priest before He is slain and says, "Father, forgive THEM for they know not what they do."
"Them" and "THEY" in John 17 are identified as the disciples, and those who will believe through their testimony. But before that, Jesus sanctifies Himself right before the cross exactly doing what the high priest under the Law is commanded by God to do.
Besides this, Saul, as rabbi and Pharisee says:
4 But when the fulness of the time was come, God sent forth his Son, made of a woman, made under the law,
5 To redeem them that were under the law, that we might receive the adoption of sons. Galatians 4:4–5.
In both passages if God wanted to atone for the sins of non-Hebrew Gentiles they would be under the Law which for centuries before Jesus the high priest ministered before God and prayed and offered sacrifices for the children of Israel - and Gentiles.
BUT nowhere does the high priest leave Israel, go to the Gentiles that surround Israel, and offer sacrifices for them and that's because Gentiles are not under the Law nor are they included in the sacrificial system of atonement instructed and commanded by God.
Gentiles are NOT atoned by Christ.
You ignored the facts
God commanded the disciples to be a light to the gentiles so that salvation would come to the ends of the earth.
Gentiles were, in fact, saved.
Romans 1:16 (LEB) — 16 For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek.
So in your theology the gentiles must be saved apart from any atonement.
And the gospel does not concern atonement.
Paul turned to the gentiles here.
Acts 13:46 (LEB) — 46 Both Paul and Barnabas spoke boldly and said, “It was necessary that the word of God be spoken first to you, since you reject it and do not consider yourselves worthy of eternal life! Behold, we are turning to the Gentiles!
Having been commanded by God
Acts 13:47 (LEB) — 47 For so the Lord has commanded us: ‘I have appointed you to be a light for the Gentiles, that you would bring salvation to the end of the earth.’
and salvation (eternal life) achieved for the gentiles as well
Acts 11:18 (LEB) — 18 And when they heard these things, they became silent and praised God, saying, “Then God has granted the repentance leading to life to the Gentiles also!”
Acts 13:48 (LEB) — 48 And when the Gentiles heard this, they began to rejoice and to glorify the word of the Lord. And all those who were designated for eternal life believed.
Your theology is contradicted by multiple verses of scripture.
Ephesians 2:11–13 (LEB) — 11 Therefore remember that formerly you, the Gentiles in the flesh, the so-called uncircumcision by the so-called circumcision in the flesh, made by hands, 12 that you were at that time apart from Christ, alienated from the citizenship of Israel, and strangers to the covenants of promise, not having hope, and without God in the world. 13
But now in Christ Jesus you, the ones who once were far away, have become near by the blood of Christ.
1 John 2:2 (LEB) — 2 and he is the propitiation for our sins, and not for ours only, but also for the sins of the whole world.
Romans 3:21–30 (LEB) — 21 But now, apart from the law, the righteousness of God has been revealed, being testified about by the law and the prophets—22 that is, the righteousness of God through faith in Jesus Christ to all who believe. For there is no distinction, 23 for all have sinned and fall short of the glory of God, 24 being justified as a gift by his grace, through the redemption which is in Christ Jesus, 25 whom God made publicly available as the mercy seat through faith in his blood, for a demonstration of his righteousness, because of the passing over of previously committed sins, 26 in the forbearance of God, for the demonstration of his righteousness in the present time, so that he should be just and the one who justifies the person by faith in Jesus. 27 Therefore, where is boasting? It has been excluded. By what kind of law? Of works? No, but by a law of faith. 28 For we consider a person to be justified by faith apart from the works of the law. 29 Or is God the God of the Jews only? Is he not also the God of the Gentiles? Yes, also of the Gentiles, 30 since God is one, who will justify those who are circumcised by faith and those who are uncircumcised through faith.
In your theology however, Christ's death must not be the way atonement or the way ransom is made for Christ died for all.
Hebrews 2:9 (KJV 1900) — 9 But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man.
2 Corinthians 5:15 (LEB) — 15 And he died for all, in order that those who live should no longer live for themselves, but for the one who died for them and was raised.
1 Timothy 2:3–6 (LEB) — 3 This is good and acceptable before God our Savior, 4 who wants all people to be saved and to come to a knowledge of the truth. 5 For there is one God and one mediator between God and human beings, the man Christ Jesus, 6 who gave himself a ransom for all, the testimony at the proper time,
He was therefore making propitiation for all the world's sin
1 John 2:2 (LEB) — 2 and he is the propitiation for our sins, and not for ours only, but also for the sins of the whole world.
but according to your theology, propitiation must not have been made through the death of Christ.