What is the ruling on a girl going to the mosque and a Quran memorization center with the intention of being nominated for marriage by one of the women, and will Allah accept her memorization and contemplation in this case?

If a servant performs a good deed for the sake of Allah and combines it with a good intention for a permissible worldly matter that does not contradict the first intention, then there is no harm in it. Examples include striving in jihad for reward and spoils, or performing Hajj while engaging in trade, or fasting for medicinal purposes. This is not considered forbidden ostentation (riya') by the consensus of scholars; rather, it is permissible. Al-Qarafi reported that such matters do not undermine the validity of the worship nor do they incur sin. Ibn Uthaymin mentioned that whoever intends both the goodness of this world and the Hereafter through their action, there is no harm in it. He added that desiring material gain does not mean ostentation, but it does reduce the level of sincerity compared to one who desires only the Hereafter. Piety (taqwa (definition)) and worship of Allah are among the causes of lawful provision, so there is no harm upon one who fears Allah and seeks sacred knowledge with the intention of relief, provision, and a good life. Similarly, there is no harm upon a woman in seeking a righteous husband and striving for that by mingling with righteous women in mosques and elsewhere, which indicates a good intention in seeking knowledge for the sake of Allah.