In Tattva Viveka, Bhaktivinoda Thakur speaks about this topic.
This work is a philosophical sally against both western and eastern philosophies including other religions like Islam, Christianity etc originally written in Bengali.
In Text 17 he says:
sarvesam nastikanam vai matam etat puratanam desa-bhasa-vibhedena
laksitam ca prthak prthak
sarvesam-of all; nastikanam-atheist philosophies; vai-indeed;
matam-view; etat-this; puratanam-ancient; desa-country; bhasa-and
language; vibhedena-with divisions; laksitam-seen; ca-and;
prthak-different; prthak-different.
From the earliest times many different varieties of atheist philosophy
have been preached in different countries and languages
He comments as follows:
1.Materialism, or the worship of material nature, 2. Idealism, and 3. Scepticism are three of the oldest kinds of atheism. All other kinds
of atheism are included within them. It is a mistake to think that the
various modern forms of atheism were all only recently invented. With
different names and in somewhat different forms, these same kinds of
atheism existed also in ancient times. Many different kinds of atheism
were thus preached in our country. Among them Sankhya, nyaya, vaisesika, and
karma-mlmamsa were openly atheistic. Patanjali's yoga philosophy and
the philosophy of Vedanta Monism (advaita) were covered atheism.
1. Sankhya :
This is an ancient philosophy expounded by pseudo-Kapila in his book.
Maharsi Kapila says in his book:
isvarasiddheh God's existence has never been proved." (Kapila-sütra
1.92)
mukta-baddhayor anyatarabhavan na tat-siddhih God is either free from
matter or imprisoned by matter. Nothing more may be said of Him."
(Kapila-sütra 1.93)
God is either free from matter or imprisoned by matter. What more may be said
of Him? If God is liberated, then no one can know anything about Him. If God is
imprisoned by matter He is not God at all.
To explain this passage the
commentator Vijnana Bhiksu says:
nanv evam isvara-pratipadaka-srutinam ka gatis tatraha
What is the meaning of the Veda passages that assert the existence of God?
In Kapila-sütra (1.96) the explanation is given:
muktatmanah prasamsa upasasiddhasya va
The descriptions of 'God' in the Vedas are actually only the praises
or worship of the liberated souls."
In this way the sankhya philosophy affirms that God does not exist.
2.Nyaya-the philosophy propounded by Gautama.
Gautama asserts:
pramana-prameya-samsaya-prayojana-drstanta-siddhantavayava-tarkanirnaya-
vada-jalpa-vitanda-hetv-abhasa-chala-jati-nigraha-sthananam
tattvajnanan nihsreyasadhigamah
By studying the different branches of logic, namely: pramana, prameya,
samsaya, prayojana, drstanta, siddhanta, avayava, tarka, nirnaya,
vada, jalpa, vitandDa, hetu, abhasa, chala, and jati-nigraha, one
attains the highest benefit."
Bhaktivinoda Thakur says:
What is the great benefit of which Gautama speaks? That I cannot see.
Perhaps he means that expert knowledge of logic is a great benefit for
the living entities. God is not included among the sixteen items he
says bring great benefit.
That is why the Vedas affirm:
naisa tarkena matir apaneya God cannot be understood by material
logic.
Gautama sees liberation in this way:
duhkha-janma-pravrtti-dosa-mithya-jnananam uttarottarapaye
tadanantarapayad apavargah
Liberation means attaining the knowledge that frees one from the
ignorance that is the birthplace of sufferings."
In general, this sutra may be seen to support the idea that liberation is the
cessation of sufferings. Spiritual bliss is not present in Gautama's conception of
liberation. In his conception there is no bliss of meeting God. For this reason
Gautama's Nyaya-sastra is opposed to the Vedas. That concludes our description
of the nyaya philosophy.
3.Vaisesika-the philosophy propounded by Kanada.
There is no need to consider this philosophy at length. In the sutras
written by Kanada it is said that there is no eternal God. Some
authors writing in the tradition of this philosophy count 'the
Supersoul residing within the individual soul who resides in the
material body' among the seven basic principles of existence. They did
that in an attempt to drive the atheism from their philosophy. Still,
in their commentaries on Vedanta-sutra, Sankaracarya and other
panditas consider Kanada's philosophy atheistic and anti-Vedic. The
truth is that any philosophy that does not accept God as the
independent supreme creator and instead posits some other conception
of God is actually atheism
4.Karma-mlmamsa-sutras-Jaimini
He did not write about God.
His primary topic was pious deeds.
He said:
codana-laksano 'rtho dharmah. karmaike tatra darsanat. The Vedas teach
religion. That religion is called 'karma' (pious deeds)."
Sridhara Svami, the commentator on these sutras, writes:
katham punar idam avagamyate. asti tad apurvam. How should this be
understood? It is understood in terms of the 'apurva'."
He says: First pious deeds are performed. Then, from those deeds the 'apurva'
(abstract secondary principle) is manifest. That apurva gives the results of the
pious deeds. Why is there any need, then, for a God to give the results of
actions?" Compte and the modern atheists have no power to say anything more
outrageous than this.
5.The Yoga-sastra is also called the Patanjala-sastra.
It was written by Patanjali Rsi.
In the Sadhana-khanda section of this book is the following sutra:
klesa-karma-vipakasayair aparamrstah purusa-visesa isvarah. tatra
niratisayam sarvajnya-btjam. sa tu purvesam api guruh
kalenanavacchedat.
God is a certain person who is untouched by suffering, karma, destiny,
or calamity. He knows everything. Because He is untouched by time, He
is the master of all."
Seeing this description of God, many may think Patanjali is a true devotee of
God.
However, at the end of Patanjali's book that mistaken impression is dispelled.
In the Kaivalya-pada section of that book Patanjali writes:
purusartha-sunyanam pratiprasavah kaivalyam svarupa-pratistDha va
citisaktir iti
When the goals of life are no more, then liberation, which establishes
the soul's original nature, or the soul's spiritual potency, is
manifest."
In the Bhoja-vrtti, this sutra is explained in these words:
cic-chakter vrtti-sarupya-nivrttau svarupa-matre 'vasthanam tat
kaivalyam ucyate
When the soul no longer has form, when it is situated in its spiritual
essence, that is called 'kaivalya' (liberation)."
This means: When the spiritual potency is situated in its own nature, that is
called kaivalya" (liberation). In this passage what is the meaning of the phrase
liberation of the spiritual potency". Does it mean here that when he attains
liberation, the individual soul no longer performs any action? Does it mean that
after he attains liberation the individual soul continues to have a relationship
with God? Unfortunately, this Yoga-sastra book does not answer these
questions? After again and again reading this book one will become
convinced that the God" described in the sadhana-khanda section is considered
only an imaginary being created to help attain spiritual perfection, and after the
soul attains perfection the idea of God is no longer taken seriously. Is this book
theistic or atheistic? You give the answer?.
6.Vedanta:
BhaktiVinoda Thakur says:
The Vedanta-sutra propounds only devotion to God. In their
commentaries on this book many atheists preached the Advaita
philosophy (impersonalism), which is covered Buddhism.
He only says this much here and elsewhere he takes up this topic.
Suffice to say from this verse:
Gaudapada Karika on Mandukya Upanishad 2.32:
न निरोधो न चोत्पत्तिर्न बद्धो न च साधकः । न मुमुक्षुर्न वै मुक्त
इत्येषा परमार्थता ॥ ३२ ॥
na nirodho na cotpattirna baddho na ca sādhakaḥ | na mumukṣurna vai
mukta ityeṣā paramārthatā || 32 ||
There is no dissolution, no birth, none in bondage, none aspiring for
wisdom, no seeker of liberation and none liberated. This is the
absolute truth.
Ultimately, there is no place for God in Advaita Vedanta.
There are Vaishnava Vedanta like Vishistadvaita, Dvaita , Achintyabheadabheda which are theistic Vedanta. There may be some theistic Shaiva and Shakta Vedantists also which I am not aware of.