There are certain schools of philosophy that exist within Hinduism that refute the idea of eternal, self-caused, creator God.
For example certain samakhya school philosophers propounded following arguments:
If the existence of karma is assumed, the proposition of God as a
moral governor of the universe is unnecessary. For, if God enforces
the consequences of actions then he can do so without karma. If
however, he is assumed to be within the law of karma, then karma
itself would be the giver of consequences and there would be no need
of a God.
Even if karma is denied, God still cannot be the enforcer
of consequences. Because the motives of an enforcer God would be
either egoistic or altruistic. Now, God's motives cannot be assumed
to be altruistic because an altruistic God would not create a world
so full of suffering. If his motives are assumed to be egoistic,
then God must be thought to have desire, as agency or authority
cannot be established in the absence of desire. However, assuming
that God has desire would contradict God's eternal freedom which
necessitates no compulsion in actions. Moreover, desire, according
to Samkhya, is an attribute of prakṛti and cannot be thought to grow
in God. The testimony of the Vedas, according to Samkhya, also
confirms this notion.
Despite arguments to the contrary, if God is
still assumed to contain unfulfilled desires, this would cause him
to suffer pain and other similar human experiences. Such a worldly
God would be no better than Samkhya's notion of higher self.
Furthermore, there is no proof of the existence of God. He is not
the object of perception, there exists no general proposition that
can prove him by inference and the testimony of the Vedas speaks of
prakṛti as the origin of the world, not God.
A lot of texts on Samakhya philosophy - such as Yoga Sutras of Patanjali do refer to the Ishvara, but they don't mean them in terms of the dualistic philosophy of someone who is a great being - creator, organizer, or destroyer. Rather, they see them as an abstract representation of someone (a special Purusha!) who is a supreme ruler (or enforcer of karma), untouched by misery, actions and desires (Yoga Sutras of Patanjali: 1.24).
The end goal of Purusha is being realized as self (Samakhya Philosophy uses Purusha-Prakriti for such), hence Ishvara being realized as self.
In contrast, Adi Shankara's Advaitic philosophy has different views on this. They believe Ishvara is an enforcer of the laws of karma.
Karma is insentient and short-lived, and cannot therefore be expected
to bestow the fruits of actions at a future time according to one’s
deserts. We do not see any insentient thing bestow fruits on those who
worship it. Therefore it is only from the Lord, who is worshipped
through actions, that their results proceed.
This is clear from Shankara's commentary of Brahma Sutras III.2, 38, 41.
In contrast to all the above, certain Upanishads and Advaita Vedanta of pre-Shankara's era, do NOT believe in laws of karma. Breaking the bondage of karma is termed as: liberation or nirvana.
For laws of Karma to exist - good karma, as well as bad karma must also exist or there must be a distinction, so as to prove/disprove them.
Right and wrong, pleasure and pain, exist in mind only. They are not
your concern. You neither do nor enjoy. You are free.
~ Ashtavakra Gita 1.6
They further deny the existence of prarabdha karma which is considered most inescapable [karma from previous birth, yielding fruits in this birth].
28-29(a). So when he knows the eternal substratum of everything and
all the universe becomes (therefore) void (to him), where then is
Prarabdha to him, the body being a part of the world ? Therefore the
word Prarabdha is accepted to enlighten the ignorant (only).
~ Nada Bindu Upanishad
Where is the unfolding of karma? Where is liberation in life, or even
liberation at death? There is only One.
~ Ashtavakra Gita (20.4)
In dualistic schools of thought, God or Ishvara is thought of as a supreme being who is the cause of Maya and also the dispenser of fruits of action, also the one who maintains the law of karma.
The ultimate goal of dualistic schools is to get over the effects of the material world and karma (both good and bad), by focusing their bhakti on Ishvara or God, hence breaking the laws of karma for them and bringing liberation. Apart from that, Ishvara is also known to reduce the intensity of karma when a devotee is absorbed in bhakti. This is evident from:
BG 3.9: Work must be done as a yajna to the Supreme Lord; otherwise,
work causes bondage in this material world. Therefore, O son of Kunti,
for the satisfaction of God, perform your prescribed duties, without
being attached to the results.
~ Bhagavad Gita (3.9)
The bhakti to Ishvara, helps the devotee to cease bondage to the material world and, hence get liberated from the material world.
In other schools of philosophy like - Jainism and Buddhism too accept laws of karma evident at multiple places without having Ishvara or God.