In a way your perception about the Non-existence of usual "Soul" in Buddhism is correct.
However, Buddha faced a popular religion 'Hinduism" around his environs which had Soul and reincarnation, with its inherent contradictions and could not get the answers to his prime investigations into human life.
Thereby he had an alternative pathway-described below:
In Buddhism, the term anattā (Pali) or anātman (Sanskrit) refers to the doctrine of "non-self", that there is no unchanging, permanent self, soul or essence in living beings.
It is one of the seven beneficial perceptions in Buddhism, and along with Dukkha (suffering) and Anicca (impermanence), it is one of three Right Understandings about the three marks of existence.
The Buddhist concept of Anattā or Anātman is one of the fundamental differences between Buddhism and Hinduism, with the latter asserting that Atman (self, soul) exists.
In Buddhism-related English literature, Anattā is rendered as "not-Self", but this translation expresses an incomplete meaning, states Peter Harvey; a more complete rendering is "non-Self" because from its earliest days, Anattā doctrine denies that there is anything called a 'Self' in any person or anything else, and that a belief in 'Self' is a source of Dukkha(suffering, pain, unsatisfactoriness).[note 1]
It is also incorrect to translate Anattā simply as "ego-less", according to Peter Harvey, because the Indian concept of ātman and attā is different from the Freudian concept of ego.[note 2]
Anatta or Anatta-vada is also referred to as the "no-soul or no-self doctrine" of Buddhism.
While the concept of soul in Hinduism (as atman) and Jainism (as jiva) is taken for granted,
which is different from the Buddhist concept of no-soul, each of the three religions believed in rebirth and emphasized moral responsibility in different ways in contrast to pre-Buddhist materialistic schools of Indian philosophies.
The materialistic schools of Indian philosophies, such as Charvaka, are called annihilationist schools because they posited that death is the end, there is no afterlife, no soul, no rebirth, no karma, and death is that state where a living being is completely annihilated, dissolved.
Buddha criticized the materialistic annihilationism view that denied rebirth and karma, states Damien Keown.
Such beliefs are inappropriate and dangerous, stated Buddha because they encourage moral irresponsibility and material hedonism.
Anatta does not mean there is no afterlife, no rebirth or no fruition of karma, and Buddhism contrasts itself to annihilationist schools.
Buddhism also contrasts itself to other Indian religions that champion moral responsibility but posit eternalism with their premise that within each human being there is an essence or eternal soul, and this soul is part of the nature of a living being, existence and metaphysical reality.
The Buddha emphasized both karma and anatta doctrines.
The Buddha criticized the doctrine that posited an unchanging soul as a subject as the basis of rebirth and karmic moral responsibility, which he called "atthikavāda".
He also criticized the materialistic doctrine that denied the existence of both soul and rebirth, and thereby denied karmic moral responsibility, which he calls "natthikavāda".
Instead, the Buddha asserted that there is no soul, but there is a rebirth for which karmic moral responsibility is a must.
In the Buddha's framework of karma, right view and right actions are necessary for liberation.