بسم الله الرحمن الرحيم
A believer is one who testifies by heart that Allah is One and there is none worthy of worship except Him, He has no partner and Muhammad is His Messenger and His slave. Also he must affirm by heart about the pillars of Islam: salah, sawm, hajj and zakah. If someone does not affirm these by heart then he shall not be counted a believer and Muslim merely by saying La Ilah Illallah.
The detail which you supplied about the said girl that she does not believe in any religion as well as she does not believe in the life after death likewise in the angels, it means that she is atheist and infidel. It is unanimous opinion of all scholars that living a marital life with a infidel girl is not lawful. Hence you should ask that girl in clear cut words that if she believes in Allah and accepts Prophet Muhammad (may peace and blessings of Allah be upon him) as the Messenger of Allah and His slave, if she believes in the tenets of Islam and other fundamentals of religion such as destiny, resurrection and life after death, angels, divine books and the messengers sent by Allah or not? If she denies, then you should immediately maintain separation from her as it is not lawful for you to pass marital life with her.
Allah knows Best!
Darul Uloom Deoband