Is it permissible to marry a girl who does not cover her face with the intention of asking her to cover it after marriage?

You should inquire about the woman's character from those who know her. If they speak well of her, then seek guidance from your Lord and propose to her. If her attire fulfills the conditions of the legal hijab (definition), then she is in a state of great goodness. As for covering the face, there is a difference of opinion among jurists, and we have favored its obligation. There is no harm in marrying her and trying to convince her to cover her face later, or stip making that a condition at the time of the marriage contract.