Every single doctrine of Hinduism rotates around absolute belief in God, without a single iota of doubt about his existence. Travelers of spiritual path, seekers believed in monotheistic aspect of God, the only one God Brahman; creator of entire cosmos.
Those indulging in religious practices (rituals) believed Sakaar form of God (having a form), a God that was Saguna (with attributes). But 100% belief in existence of God was there in both cases.
Why does Hinduism believes in existence of God be seriously?
Scientists in western world until few decades before disputed big bang theory! But in Upanishads (independent spiritual chastises) everything from origin of cosmos to dissolution of cosmos (Pralaya in Hinduism) is minutely detailed.
As per Upanishads the present cosmos came into being when God Almighty (Brahman) exploded self with a big bang. The Upanishads evolved between 3500 to 5000 years before now may be more. None in India (or erstwhile Bharatvarsha) could ever repudiate the findings of Upanishads. Everything contained in Upanishads even Vedas directly came from God.
With the occurrence of big bang when Brahman explodes self, all pure souls’ atmans scatter all over cosmos at unimaginable speeds. In the melee hurtling souls atmans gathered impurities. To cleanse self of dross impurities within, regain its lost original pure prime pristine primordial form starts cosmic life cycle of every soul atman.
Only when life supporting planets like mother earth evolved souls atmans immediately started manifesting life. Starting from form of amoeba (single cell formation), life further evolves into multi-cell formation, insect life, plant life, animal life and finally the human form.
Human beings are the highest manifest stage in cosmic life cycle. It is only in human form a soul atman liberates forever from cycle of birth and death, becoming a pure soul atman again.
In absence of belief in god, the existence of entire cosmos becomes questionable!
From spiritual angle definition of God Almighty is, sum total of all souls atmans in cosmos in their pure form. This collective power, energy is what explodes at the time of big bang.
If we exist, so does souls atmans and also God Almighty, Brahman.
Although none can see God but it exists. Enlightened ones could establish communion with God all the time on one-to-one basis. Mahavira could do it and so could Gautama Buddha. Even Jesus Christ could do it followed by Prophet Mohammed.
In recent times Sri Ramakrishna Paramhansa and Maharshi Ramana successively succeeded reaching God in their lifetime.
Anyone who realizes self realizes god can establish communion with God every second of life.
Doctrine of Advaita Vedanta by Adi Shankaracharya
In the doctrine of Advaita Vedanta propagated by Adi Shankaracharya, Adi Shankaracharya proves that other than God Almighty nothing existed in cosmos. The physical world existed only in thoughts of God Almighty but due to act of Maya (veil of illusion) everything appeared real.
Let us presume that God exists then who created God? If the present world (entire cosmos) has a boundary, then what beyond! As the present cosmos does not seem to have a boundary it could exist only in thoughts of God Almighty similar as an image in the major.
The doctrine of Advaita Vedanta further says broken down to basic building block of cosmos, the whole world was gaseous in formation. The whole visible world was made up of clusters of atoms and molecules. Only when viewed from senses point of view, things appeared solid, in reality all was pure gaseous formation.
As Hinduism beliefs in pure logic, contemplating on philosophical precepts of life we would finally agree that God exists and so does world of souls’ atmans.