Dear Hadi,
Dear Reader,
Thank you for your question. Tahajjud prayer, a voluntary nighttime prayer, is considered a highly rewarding act of worship. This prayer is open to all. That being said, there is no specific link between it and your question about marriage.
You can of course pray tahajjud and make du’a, asking God to accept your repentance for any transgressions, and committing yourself to not repeat them.
We remind you that Allah SWT stresses that the door to repentance is always open, even after the gravest of sins. This is stated, among other places, toward the end of Surat al-Furqan, discussing the qualities of the believers:
They are those who do not invoke any other god besides Allah, nor take a human life - made sacred by Allah - except with legal right, nor commit fornication. And whoever does any of this will face the penalty. Their punishment will be multiplied on the Day of Judgment, and they will remain in it forever, in disgrace. Except for those who repent, believe, and do good deeds, they are the ones whose evil deeds Allah will change into good deeds. For Allah is All-Forgiving, Most Merciful. (Quran 25:68-70).
Therefore, we believe the focus should be on a sincere repentance, that includes desisting from any haram behavior and asking God for forgiveness. With God’s mercy, your repentance insha’Allah will be accepted, and any haram deeds may be changed to good, and we see no reason why you cannot then proceed with marriage to the young woman with whom you were involved.
In peace.