What is the atonement for one who was with a non-Jewish woman?

Hello and blessings.

As you wrote, the main atonement is your repentance and your commitment to strengthen and elevate yourself.

Repentance is beneficial for all sins, and this is the essence of atonement, as it is explained in the verse in Isaiah 55:7

7) Let the wicked forsake his way, and the man of iniquity his thoughts; and let him return unto Hashem, and He will have mercy upon him; and unto our God, for He will abundantly pardon.

Therefore, when a person accepts upon themselves not to return to this sin ever again, they no longer have a connection with that sin.

I will quote for you from the words of the Rambam in Hilchot Teshuvah, Chapter 7.

Halacha 4:
And let no person think that a ba'al teshuvah (one who has repented) is distanced from the level of the righteous because of the sins and transgressions he has committed; this is not the case. Rather, he is beloved and pleasant before the Creator, as though he had never sinned at all. Not only that, but his reward is greater, for he has tasted the taste of sin and separated from it and has subdued his desire. The sages said, in the place where ba'alei teshuvah stand, even completely righteous people cannot stand, meaning their merit is greater than those who have never sinned because they have conquered their desires more than them.

Halacha 6:
Great is repentance, for it brings a person closer to the Shechinah (Divine Presence), as it says, Return, O Israel, unto Hashem your God; and it says, But you returned not unto me, saith Hashem; and it says, If you return, Israel, saith Hashem, you shall return to me. This means that if you return in teshuvah, you will cleave to Me. Repentance brings close those who were far away. Yesterday, he was despicable before the place, abominable and distant, and today he is beloved and pleasant, close and dear.

Halacha 7:
How excellent is the merit of repentance! Yesterday, he was separated from Hashem the God of Israel, as it is said, Your iniquities have separated between you and your God; he cries out but is not answered, as it is said, For when you multiply prayer, I will not hear; and he performs commandments and they are cast before Him, as it is said, Who asked this of you, to trample my courts? Who also is among you that would shut the doors? And today he is attached to the Shechinah, as it is said, And you who cleave unto Hashem your God; he cries out and is answered immediately, as it is said, And it shall come to pass, that before they call, I will answer; and he performs commandments and they are received with satisfaction and joy, as it is said, For God has already desired your deeds.

Moreover, there is a matter of the purification of the soul, which two hundred years ago was very common to do through fasts and austerities. However, in recent generations, the righteous ones with divine spirit revealed that giving charity from time to time, not necessarily large sums, rectifies everything, and one can also achieve the purification of the soul as if he never sinned.

Additionally, it is written in the books that regarding this it is said that anyone who observes Shabbat properly, even if they serve idolatry like the generation of Enosh, they are forgiven.

I will also quote to you the words of Rabbeinu Yonah in Sha'arei Teshuvah, Book of Sha'arei Teshuvah, the fourth gate - letter 11:
And if a person transgressed on the prohibitions subject to excision and the death penalties of the court and he repented, after all, sin is not atoned without suffering, as repentance depends on it, and suffering purifies. He should prepare his heart to perform the commandments that defend against suffering, such as the commandment of charity, for it saves from death, as it is said (Proverbs 10:2), And charity delivers from death. And one who has no money to give charity, should speak well of the poor man, and have others help him. Our Rabbis, of blessed memory, said (Baba Batra 9:1), Greater is the one who does (good deeds) than the one who gives charity. Likewise, he should engage in the commandment of acts of kindness to help his friends with his advice and efforts, as our Rabbis, of blessed memory, said (Sukkah 49:2), Great is acts of kindness than charity, for charity is with his money, and acts of kindness is both with his body and with his money, and charity is only for the poor, while acts of kindness apply to both the poor and the wealthy. Likewise, he should speak kindly to the poor and honor him and comfort him from his distress, as it is said (Isaiah 58:10), And if you draw out your soul to the hungry. Our Rabbis, of blessed memory, said (Baba Batra 9:2), for he who pacifies with words is greater than he who gives charity. He should also engage in the commandment of visiting the sick and burying the dead and comforting mourners and making happy the bride and groom, as all of these are ways of kindness.

And all the advisements we have mentioned are generally included under what King Solomon, may peace be upon him, said (Proverbs 16:6), By mercy and truth iniquity is purged, for the acquisition of the Torah is called the acquisition of truth, as it is said (Proverbs 23:23), Buy the truth and sell it not. And it is said (Psalms 119:151), And Your Torah is truth.

And our Rabbis, of blessed memory, said (Leviticus Rabba, Kedoshim 25:1), It is a tree of life to those who hold fast to it (Proverbs 3:18), If a man transgressed on prohibitions subject to excision or death penalties, if he was accustomed to read one chapter a day, let him read two chapters. If he was accustomed to read one parsha, let him read two parshiot. And from both sides, the Torah will protect them from suffering. One reason is because our Rabbis, of blessed memory, said (Shabbat 127:2), The study of Torah is equivalent to all.

And the second reason is that he will invest his efforts in the Torah and toil in it and that which will cause him to lose sleep from his eyes will elevate him in place of suffering, as our Rabbis, of blessed memory, said (Sanhedrin 96:2), All bodies were created for labor; happy is he who labors in Torah.

And they said (Sanhedrin 26:2), Why is it called the name Tushiyah? Because it strengthens the power of a person.

There are atonements that great leaders of Israel do to atone for these sins, which include prayers and requests. If you have the ability to participate in one of them, how good it is, but the essence is as I have stated.

With blessings - Binyamin Shmueli