Is it permissible to supplicate that God show a woman a sign or a glad tiding that a specific young man will be her righteous husband?

There is no harm in a woman supplicating to Allah to grant her a righteous husband. However, it is preferable not to specify, because a person does not know what is good for them and what is bad. Therefore, they should entrust their affairs to Allah, seek His guidance (Istikhara), and ask Him for success without specifying. For a person may dislike something that is good for them and love something that is bad for them, and "Allah knows and you do not know."