Obviously, demographically Asia was the most likely continent for a religion to appear because it had the largest population. However, it still seems to me that something else must have skewed things to make a religion more likely to grow if it came from Asia.
this question could also be posted to r/explaintomethesocioligyofreligion, but I wonder if any historians can offer an explanation?
Since your question has an enormous scope, this answer is going to necessarily be inadequate. Religions grow by conversion and through normal demographic growth (even in the post-industrial West, most people at least nominally identify with their parents' religion). I'm not sure how to define "major religions" without offending people, so here's my offensive working definition: a religion with more than a billion adherents.
I cannot say anything about Hinduism or Buddhism without betraying my own staggering ignorance, so I'll defer that part of the answer. And focus on Christianity and Islam, and mostly on their early stages because their later conversion efforts in sub-Saharan Africa and the Americas wouldn't have been possible without the foundation.
Both religions actively proselytize (try to convert non-members) and have spread ridden the coattails of empires to spread. Constantine's decriminalization and then promotion of Christianity eased its spread throughout the Roman Empire and later Emperors in the East and West actively promoted Christianity and at times persecuted pagans and Jews. The rise of Islam and the Arab conquest of the Middle East occur at the same time (there are differing interpretations as to which was the cause and which the effect) but in either case there was a Muslim, Arab elite politically dominant over lands stretching from Spain to Pakistan. As time went on local populations converted and grew.
The religions displaced by Christianity and Islam were largely ethnically bound. The Romans weren't preoccupied with enforcing Roman religion (beyond the cult of the emperor) throughout the empire. Zoroastrianism has a reputation as being a formalistic religion tied to the elites, I'm not aware of any attempts to spread that faith outside of Persia.
tl:dr Religions spread through conversion and having lots of kids, religions that seek converts grow.
sources: Muhammad and the Believers by Fred Donner The Venture of Islam vol 1. by Marshall G S Hodgson Lars Brownworth "12 Byzantine Rulers - Constantine" podcast
First we need to define what religion is. Simply stated religion is a particular worldview (there are more to this, but for the sake of discussion this will do). This means that adherents of Atheism, Agnosticism all have their own religion too.
Going by that definition, every culture has a religion. Its only that, over the course of history religions originating from Asia have dominated the field.
Why these major religions came to dominate, is a whole different topic in itself.