This is actually a fairly complex question to work out.

In order to fully understand this question, we'd have to work out exactly what a religion is. To save you from a long answer, religion today is not really representative of the religions found before around 300-700 AD (this is an approximation based upon, among other things, when monotheism and the idea of omnipotence first began gaining some popularity). The "archaic" religions were more involved in superstition, folklore and, later at least, a very loose relationship with the gods. It should be noted though that this relationship with the gods was more of a relationship built out of symbolism, identity, and superstition than one built out of faith and/or the concept of enlightenment (enlightenment should not be confused with shamanism which was—as I would argue it—fundamentally different). Furthermore, societies rarely, if ever before the rise of monolarity, believed in a set number of gods. The number of gods, and even the characteristics and stories pertaining to those gods, was open for reinterpretation.

Okay so that gave us a basis necessary to understand why this question is so much more difficult to answer. These early "religions" were not defined, and as such were not necessarily in competition with one another. Societies could be in competition with one another, and they could claim that their gods were therefore in competition with one another, but the word I'd like to stress is competition. To imply competition, which was overtly implied and accepted in most of, at least, the western world, is to imply that no one religion necessarily disputed the legitimacy of another. Furthermore religions were actually used, quite often successfully, as a tool for conquest and alliance. When one society conquered another, in order to avoid the indigenous people feeling alienated or an adversary to the new establishment, conquerers would often actually claim that their two religions were really the same. "You have a sea god named Waveman? We have a sea god named Surfbro." The same was also often done when two city states or societies decided to trade or form an alliance.

The point of this all really is to show that "religion," which is considered relatively structured and unchanging today (I'd argue otherwise) is a new concept. The cool thing about polytheism and to an extent monalarity, is its ability to coexist with other religions because of its lack of identification as a more "Correct" religion—this isn't to say, though, that wars or disputes never occurred because of religion; they did, though not on the basis of one being correct or the other not, more often it was on the basis of one society supporting a god whom another society viewed in an unfavorable light. So basically no. No because one one hand there was no religion, necessarily, that was truly uniform and structured as there is today.

Edit: If you're interested in this subject, I would highly recommend "The Evolution of God" by my all time favorite author: Robert Wright. Actually if you're interested in darwinian logic being applied beyond physical, biological evolution, read Robert Wright—seriously.

TLDR; No, kind of, pretty much; It's complicated, but no.

I think Zoroastrianism would be the best contender for your answer. There's considerable uncertainty about when Zoroaster himself lived, including dates anywhere from 1500 to 500 BC. However his ideas eventually caught on and Zoroastrianism was well established by the founding of the Achaemenid Empire in 550 BC under Cyrus the Great. Note only that, Zoroastrianism became the dominant religion in the region backed in part by state support (though the Achaemenid rules showed remarkable religious tolerance and support in contrast to their predecessors), at a time and place that saw the Achaemenid Empire occupy a significant land mass, stretching from Egypt to Turkey to modern-day Afghanistan and Pakistan in the east.

Furthermore, although Zoroastrianism suffered some setbacks from Alexander the Great's conquest, it was strong enough to survive, and was the main religion under the Parthians (247 BC - 224 AD), before became the state religion under the Sasanian Empire, which lasts 224 - 651 AD, and encompassed much of the same area as the earlier Achaemenids, but with more expansion in Central Asia. Zoroastrianism closely bound religion and state in the Empire. This lasted basically until the Arab expansions under Islam in the mid 7th century.

So as the dominant religion in one of the world's largest land empires in a region for over a millenium, you could definitely number Zoroastrianism up with the 'big world religions'.