Arguments against Atheism in the Hindu tradition :

How have Vedantic thinkers countered "Nastika" arguments be it from Charvakas, Lokayatas or Buddhists over the centuries? What is the HIndu counter to Atheism?

Here's a thread on the same. Feel free to contribute!
At around the beginning of the Vikram Samvat era (~200BCE to ~200 CE), there emerged a sage in Northern India named Badarayana (sometimes conflated with Veda Vyasa) who authored the "Brahma Sutras" - a set of 555 aphorisms that provide clues to understand Upanisadic teachings
In the second chapter of this foundational Vedanta text, there are a couple of verses in which can be found one of the earliest Hindu arguments against atheism. These are verses 2.1.32 and 2.1.33 (Contd..)
"न प्रयोजनवत्त्वात्।।2.1.32।।

Translation : "Not on account of having a motive"

This Sutra presents the "Purvapaksha" argument of atheists on why "Brahman" (loosely "God") cannot be the cause of creation. It is arguably the strongest atheistic statement in Vedantic literature
Some 800 years later, Sankara in his commentary elaborates on this Sutra -

"God is possessed of all powers of creation. But nobody engages in anything without a motive. Every task is undertaken to satisfy a desire. (Contd..)
"But given that Brahman is self-sufficient, it has nothing to gain from creation. Hence Brahman cannot be the cause of this world”

So Sankara is presenting the argument of atheists, on why there is no Brahman. God by definition is bereft of desire. Hence he cannot create.
But in the very next Sutra (2.1.33), Badarayana demolishes the Purvapaksha view!

"लोकवत्तु लीलाकैवल्यम्।।2.1.33।।

Translation: “But (it is) mere sport, as in ordinary life.”

(Contd..)
What does this mean? Now let's seek another Vedantin Ramanuja's help to understand this sutra -

"“The motive which prompts Brahman to the creation of a world is nothing else but sport, play. " (Contd..)

"
"We see in life how some great poweful king, has a game at balls, from no other motive than to amuse himself; hence there is no objection to the view that sport only is the motive prompting Brahman to the creation, sustentation, and destruction of this world”
So this is something novel in the history of theology. Here’s a verse that is viewing creation as a sport, as a pastime (Leela) , engaged in by the supreme soul, notwithstanding its perfection and self-sufficiency
Sutra 2.1.33 is very important in Indian intellectual history as it is the first use of the term "Leela" in Indian literature. Leela is a word that would capture the imagination of Indian theologians, for the next millennia, and give rise to the Bhakti movement in the middle ages
These two aphorisms of Badarayana present a unique challenge to Atheism - where the Purvapaksha is presented respectfully and then taken apart by bringing in the concept of "Leela" - in some ways unique to India. (though I may be wrong here).

(Contd..)
I am sure there have been other arguments against atheism in the Indian tradition, besides the one I described. Feel free to chip in!
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