"Buddha does not claim to be a creator of lives or the Universe.", true?

Ven and good Buddha-Parisata,

In the case on whould say that the "Maha-Brahma Buddha" did not create existances and worlds, one would speak wrongly about the Tathagata.

This was said by the Blessed One, said by the Arahant, so I have heard: "I am a brahman, responsive to requests, open-handed, bearing my last body, an unsurpassed doctor & surgeon. You are my children, my sons, born from my mouth, born of the Dhamma, created by the Dhamma, heirs to the Dhamma, not heirs in material things... iti 100

He of course did not address those not related to him, outsiders, being still children, relatives of Mara.

And in this way he is also regarded by those in relation to the Tripple Gems. Without relation to him and his heritage, the Dhamma carried by the Sangha, one can never be helped by the Tripple Gems, having the Buddha as it's origin.

Other then ideas of people thinking they can just use what comes along, people of ingratitude, of no integrity, unrelated, the Buddha taught depended origin and right view, never denying duties in relations, parents, Brahmas, giver, goodness ...

He has right view and is not warped in the way he sees things: 'There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions. There is this world & the next world. There is mother & father. There are spontaneously reborn beings; there are brahmans & contemplatives who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is how one is made pure in three ways by mental action." ...(AN 10.176)

Depending "creation":

It is in dependence on me (the Buddha) as an admirable friend that beings subject to birth have gained release from birth, that beings subject to aging have gained release from aging, that beings subject to death have gained release from death, that beings subject to sorrow, lamentation, pain, distress, & despair have gained release from sorrow, lamentation, pain, distress, & despair. (Upaddha Sutta)

Feel given to ask for further explainings if still doubt and wishing to erase it.

(Note that this is not given for trade, exchange, stacks, entertainment and akusala deeds, but as a share of merits and to continue such for release)

The Buddhist universe is cyclically created and then destroyed, a process which has no beginning. In the era of creation a "primordial wind" is said to generate the universe

The Vivartakalpa begins with the arising of the primordial wind, which begins the process of building up the structures of the universe that had been destroyed at the end of the last mahākalpa. As the extent of the destruction can vary, the nature of this evolution can vary as well, but it always takes the form of beings from a higher world being born into a lower world. The example of a Mahābrahmā being the rebirth of a deceased Ābhāsvara deva is just one instance of this, which continues throughout the Vivartakalpa until all the worlds are filled from the Brahmaloka down to Naraka.

In a similar way to how fire usually destroys the universe.

Obviously, the processes of rebirth themselves (rather than the world they inhabit) are driven by karma.

There is no "creator God" in Buddhism. There are many gods, but these gods are not self subsisting, and will be reborn as something else.

I'm not very familiar with the idea of "primal Buddhas", but because ignorance is beginningless it would be wrong to say phenomena are created by, rather than emanate etc., from them.

The Buddha is one who discovers the 4 Noble Truths with one's own efforts unguided by a teacher or previous teachings. The Buddha does not create any creatures or the universe.

Creatures and the universe is created by cause and effect. This is a self-sustaining law this does not need a lawgiver or mediator.

According to the Dona Sutta (quoted below), the Buddha does not play any role like a creator or sustainer or even as a creature in the universe.

He is simply awake.

"When asked, 'Are you a deva?' you answer, 'No, brahman, I am not a deva.' When asked, 'Are you a gandhabba?' you answer, 'No, brahman, I am not a gandhabba.' When asked, 'Are you a yakkha?' you answer, 'No, brahman, I am not a yakkha.' When asked, 'Are you a human being?' you answer, 'No, brahman, I am not a human being.' Then what sort of being are you?"

"Brahman, the fermentations by which — if they were not abandoned — I would be a deva: Those are abandoned by me, their root destroyed, made like a palmyra stump, deprived of the conditions of development, not destined for future arising. The fermentations by which — if they were not abandoned — I would be a gandhabba... a yakkha... a human being: Those are abandoned by me, their root destroyed, made like a palmyra stump, deprived of the conditions of development, not destined for future arising.

"Just like a red, blue, or white lotus — born in the water, grown in the water, rising up above the water — stands unsmeared by the water, in the same way I — born in the world, grown in the world, having overcome the world — live unsmeared by the world. Remember me, brahman, as 'awakened.'

Two suttas come to mind.

Assu Sutta (SN 15.3)

At Savatthi. There the Blessed One said:

"From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. What do you think, monks: Which is greater, the tears you have shed while transmigrating & wandering this long, long time — crying & weeping from being joined with what is displeasing, being separated from what is pleasing — or the water in the four great oceans?"

Brahmajāla Sutta (DN 1):

40. "But sooner or later, bhikkhus, after the lapse of a long period, there comes a time when this world begins to expand once again. While the world is expanding, an empty palace of Brahmā appears. Then a certain being, due to the exhaustion of his life-span or the exhaustion of his merit, passes away from the Ābhassara plane and re-arises in the empty palace of Brahmā. There he dwells, mind made, feeding on rapture, self-luminous, moving through the air, abiding in glory. And he continues thus for a long, long period of time.

41. "Then, as a result of dwelling there all alone for so long a time, there arises in him dissatisfaction and agitation, (and he yearns): 'Oh, that other beings might come to this place!' Just at that moment, due to the exhaustion of their life-span or the exhaustion of their merit, certain other beings pass away from the Ābhassara plane and re-arise in the palace of Brahmā, in companionship with him. There they dwell, mind-made, feeding on rapture, self-luminous, moving through the air, abiding in glory. And they continue thus for a long, long period of time.

42. "Thereupon the being who re-arose there first thinks to himself: 'I am Brahmā, the Great Brahmā, the Vanquisher, the Unvanquished, the Universal Seer, the Wielder of Power, the Lord, the Maker and Creator, the Supreme Being, the Ordainer, the Almighty, the Father of all that are and are to be. And these beings have been created by me. What is the reason? Because first I made the wish: "Oh, that other beings might come to this place!" And after I made this resolution, now these beings have come.'

Canonically the Buddha is credited with [re]discovering the Dhamma, and (I presume) with creating the Sangha and the Vinaya.

But I think the statement "Buddha does not claim to be a creator of lives or the Universe" was meant to be viewed in context, where the content was, "Difference From Other Religions":

• There are, other religions which teach e.g. that "God created heaven and earth" or perhaps that "God created human's souls".
• Conversely I think that Buddhism doctrine is that the origin of samsara is "an unanswered question", and even that people inherit their own karma. The Buddha acted as a teacher, a leader, a worthy example.