I had mentioned
Carvaka several posts ago. Dating from around the time of the founding of Buddhism and Jainism, it already held many of the tenets of an atheistic religion:
1. All attributes that represent a person are contained in their physical body. Therefore, there is no soul independent of the body, or any afterlife. There is no heaven, hell, or reincarnation.
2. There are no supernatural causes for natural phenomena, everything has a natural cause. Therefore there are no gods or supernatural entities.
3. There is nothing wrong with pleasure derived from the senses. Austerities accomplish little or nothing.
4. The Vedas (foundations of Vedic religion) were created by men and have no inherent authority. Rituals based on them also accomplish nothing.
5. In general, truth, integrity, consistency, and freedom of thought are held as the highest philosophical virtues.
This is about all that is known of the Carvaka tenets, almost all of their writings have been lost. The remaining writings consist of about 60 verses known as the
Barhaspatya sutras, with an unknown number of additional verses possibly still extant but uncollected.
From the same time is the
Ajivika school. Followers of this philosophy were strict determinists, and most followers were non-theistic or atheistic. They held that time was an illusion, since all events -- past, present and future -- were already fixed.
This school was actually quite popular for a time, rivaling Buddhism and Jainism, until Ashoka ordered the execution of all Ajivikas in territories ruled by him. (He evidently regarded Ajivika as a serious threat to Buddhism, and decided that it needed to be destroyed.) As with the Carvaki school, almost all their writings have been lost.
It is commonly accepted that both of these schools appeared at the same time as, or slightly before, Buddhism and Jainism, since both religions appear to have incorporated a number of ideas from them.
This would also make them somewhat earlier than similar Greek philosophies. I would not be surprised to learn that there was a flow of ideas from India to the Greek-speaking lands at that time. Could the Greek development of rationalism in general have been inspired by the Indian schools?
If Ashoka had not suppressed the Ajivika school, it might have survived to the present day, possibly merging with the Carvaka school to form an early materialist scepticism. In fact we could possibly have seen an early flowering of the scientific method, at about the same time as the Hellenistic version -- and this version might have survived!
edit -- Actually, most of the pieces of a full-fledged scientific revolution were already in place at that time, from philosophy (discussed above) to mathematics, for example
Panini (520-460 BCE) who developed Boolean logic and the foundations of programming language,
Pingala (3rd century BCE) who studied combinatorics, binomial coefficients and Fibonacci numbers, and
Katyayana (3rd century BCE) who produced results in geometry. I am now curious why a scientific revolution did NOT develop in India at the same time as in Greece, unless one did happen but has been since forgotten.