Is it permissible to entrust a polytheistic woman to God—with the intention of guiding her—based on the noble Hadith: "Whoever entrusts something to Allah, He preserves it for him"?

It is not permissible to love a polytheist woman or a disbeliever who insists on her disbelief, just as it is not permissible to pray for a disbeliever for forgiveness or mercy. However, it is permissible to pray for her guidance.

It is not permissible to remain in an illicit relationship with her. Rather, you must invite her to Islam according to Sharia guidelines, without seclusion or speaking in a soft manner. If she responds, then praise be to Allah. Otherwise, you cannot guide someone you love, for guidance is in the hand of Allah. If she does not embrace Islam, her destiny is the Fire.

You should strive to invite her [to Islam], for inviting one person to guidance is better than red camels. It is preferable that women undertake the task of inviting her, fearing falling into sin.