All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If a man proposes to a woman or if a woman intends to offer herself in marriage to a man, it is prescribed in this case to perform the Istikhaarah (divine guidance-seeking prayer), as stated in the relevant Hadeeth reading: “When any of you intends to do something…” [Al-Bukhari] The Istikhaarah prayer is prescribed for a person who is determined to do something.
However, if neither of the two parties has proposed in marriage, then there is no point in performing the Istikhaarah prayer because it is a special supplication to be recited in a specific case and manner, as explained in Fatwa 81434.
There is nothing wrong if a woman supplicates Allah, The Exalted, to facilitate her marriage to a righteous man in general (without specifying a certain person).
For more benefit on Istikhaarah prayer, you may also refer to Fataawa 173969 and 172573.
Allah Knows best.