I have read about the difference between "croire à" and "croire en" in other questions.
- croire à qqch: to believe in the existence or veracity of sth (sth. may be a fictional character or a group of people)
- croire en qqch/qqun: to have trust/faith in sth./sb. It is the one idiomatically used to express faith in the existence of God.
My understanding is that "to have faith in sth which is not proven to exist" is identical "to believe in its existence". Is that right? If so, both sentences below are identical.
Je crois à l'existence de Dieu/extraterrestres.
Je crois en l'existence de Dieu/extraterrestres.