Just a little clarification. The religion at the time is Brahmanism (aka the Vedic religion). The various schools of Hinduism are the offspring of Vedicism, while Buddhism and Jainism are often thought to derive from the parallel non-Vedic Shramana movement.
Now atheistic thinking was not foreign to Indian thought even before Buddhism. Traditionally, different Indian philosophies were classified depending on whether they accept the Vedas as authoritative or not: those who did were considered to be ‘orthodox’ and called astika ‘it is so’, while those who did not (like Buddhism and Jainism) were labelled nastika “it is not so.” Sometimes this is translated as ‘theist’ and ‘atheist’, respectively, but this is slightly incorrect, since while the three nastika schools rejected the notion of the existence of a creator god alongside the authority of the Vedas, at least one or two astika schools (the Samkhya and the Mimamsa, at least in its early stage) thought the same while accepting the Vedas. One must keep in mind though that the type of atheism espoused in historical Indian philosophies is different from the Western kind we are familiar with today: the Samkhya school for example believed in a dualistic existence of prakriti (“nature”) and purusha (“spirit”) and had no place for an Ishvara (“god”) in its system. The early Mimamsa school saw no need for the existence of an Ishvara because of its karma-centered philosophy: it is thought that human action (karma; in this case, performance of Vedic rituals) was enough to generate the necessary circumstances (the “unseen” or adrishta) for the enjoyment of its fruits.
I would like to expand on my own post.
Āstika and
nāstika, as mentioned, were terms used to classify philosophical schools and persons, according to whether they accept the authority of the Vedas or not.
Traditionally, there were six ‘orthodox’
āstika schools:
Nyāya,
Vaiśeṣika,
Sāṃkhya,
Yoga,
Mimāṃsā (aka Pūrva Mīmāṃsā), and
Vedanta (aka Uttarā Mīmāṃsā). Sometimes these are often coupled into three groups for both historical and conceptual reasons: Nyāya-Vaiśeṣika, Sāṃkhya-Yoga, and Mimāṃsā-Vedanta. Mimāṃsā’s primary enquiry was into the nature of
dharma (here meaning ‘duty’, i.e. a set ritual obligations and prerogatives to be performed properly) based on close hermeneutics of the Vedas, while the Vedantic tradition focused on the esoteric teachings of the
Āraṇyakas and the
Upanishads. Sāṃkhya held that knowledge is the means of liberation, while Yoga was more of a system of active striving, mental discipline, and dutiful action. Nyāyá was a form of logic and epistemology, since its main tenet was that valid knowledge (obtainable through perception, inference, comparison, and testimony) was the only way to obtain release from suffering, while Vaiśeṣika espoused a form of
atomism: everything in the universe are reducible to a finite number of atoms.
As mentioned, Sāṃkhya and Mimāṃsā do not hold to the existence of a supreme creator or controller (
Īśvara). The Sāṃkhya school was dualistic: it held that there are only two realities in the universe, namely
puruṣa (the ‘spirit’/‘self’) and
prakṛti (‘nature’). Atheistic strands of Mimāṃsā meanwhile held that the Īśvara’s existence is ultimately unnecessary, just as there was no need for an author to compose the Vedas or a god to validate the rituals. It argued that the Vedic deities even have no existence apart from the
mantras that speak their names. Performance of rituals (
karma or ‘action’) was enough to generate the necessary circumstances; the power of the mantras is what is seen as the power of the gods.
There were three main
nāstika schools:
Cārvāka,
Jainism and Buddhism. In addition to their rejection of the Vedas, all three are also ‘atheists’ (in the Indian sense) in that they did not believe in a supreme Īśvara who created and maintains the world.
The so-called
Śramaṇa (Pali: Samaṇa) was a parallel movement which existed alongside the ancient Vedic religion. This tradition was what gave rise to Jainism and Buddhism (among the
nāstika) and Yoga (among the
āstika), and was responsible for the ideas of
karma,
saṃsāra (the cycle of birth and death) and
moksha (liberation from that cycle). It mainly refers to renunciate ascetic traditions which were individual, experiential and free-form traditions, independent of society in religious competition with Brahmin priests, who as opposed to Shramanas, stressed on mastery of texts and performing rituals.