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.
The fact is as you mentioned in your question that Islam does not approve any relationship between a man and a non-Mahram woman as known nowadays. Staying alone with a non-Mahram woman is forbidden in the Sharee’ah. The Prophet said: “No man should stay with a lady in seclusion and a woman should not travel alone without being accompanied by her Mahram (unmarriageable male relative or a husband).” [Al-Bukhari]
Know that a good and honest intention does not make lawful what is made unlawful by Allah and His Prophet .
Therefore, we advise you to keep yourself away from this girl and avoid mixing with her. On the other hand, it is permissible for you to help her if you can do so without socializing with her, such as guiding her to an Islamic center to take care of her.
It is also permissible for you to marry her in the presence of her available guardian if there is any; otherwise, an Islamic center at that place can marry her off to you. In fact, you may be rewarded for this act, Allah willing.
Allah knows best.