I understand in the first Amud of Masechet Sotah, an individual’s future [first] spouse is predestined. Is there a possibility of praying to Hashem, such that one may change the decree and designate a particular person for marriage?
The gemara in Moed Kattan 18b would seem to advise against it:
כי הא דרבא שמעיה לההוא גברא דבעי רחמי ואמר תזדמן לי פלניתא א"ל לא תיבעי רחמי הכי אי חזיא לך לא אזלא מינך ואי לא כפרת בה' בתר הכי שמעיה דקאמר או איהו לימות מקמה או איהי תמות מקמיה א"ל לאו אמינא לך לא תיבעי עלה דמילתא
This is like this incident, in which Rava heard a certain man asking for mercy, i.e., praying, who said: Grant me so-and-so as a wife. Rava said to him: Do not pray and ask for mercy in this way. If she is fit for you, and it has been decreed that she will be your wife, she will not go away from you. And if she is not destined to be your wife, you will come to deny the Lord when you see that your prayer is not answered. After the man married this woman, Rava heard him say in prayer: Please either let him die before her or let her die before him. He was speaking about himself and his wife because he had grown to hate her so much. Rava said to him: Did I not say to you not to pray for this matter?
Nothing can be done to change the zivug
Rashi explains that Rava was concerned that the woman would die, from which we see that nothing can be done to change a zivug.
One of the Tosafot (a talmid of Rabbi Yechiel of Paris, in Nimukei Yosef) posits that prayer can alter the zivug but it will eventually end in disaster in order that the true zivug take place.
Perhaps the zivug could be changed
The Ritva is of the opinion that prayer and extraordinary deeds can change one’s zivug without harm and the reason that Rava discouraged him was because he saw that it would not be a good match.
All would agree, however, and this is the accepted approach, that one could pray that IF a particular woman is his zivug, that G-d enable the match to take place at the best time and in the best way possible.
R' Ullman also quotes the Zohar's opinion on this matter:
The Zohar (Vayechi 229a) states, “According to one’s deeds G-d matches couples. If a man perverted his ways, his zivug is given to another, until he rectifies his ways. When he rectifies his ways and his time has come, the other man is pushed aside and he comes to takes what is his. This is the most difficult task for the Holy One, blessed be He, to banish one man because of another”.
This suggests that in a case of what seems to be a “mistaken” match, one’s primary effort should be expended in teshuva and making oneself righteous while waiting for G-d to decide if he is in fact the right one and whether he is meritorious enough to deserve the woman he thinks is his zivug.
R' Ullman writes that all would agree (and this is the accepted approach) that one could pray that IF a particular woman is his zivug, that G-d enable the match to take place at the best time and in the best way possible.
Key word here being "IF"- ie one shouldn't specifically daven "FOR" a specific woman to be his zivug.