First, some canonical background:
According to the Acintita Sutta, speculating on the origin of the cosmos or similar topics will lead one to confusion i.e. it cannot be understood.
According to the Cula-Malunkyavada Sutta in the Parable of the Poisoned Arrow, the speculation of the origin of cosmos or suffering or similar topics is not useful, because the more important and urgent matter is to attend to the topic of suffering.
According to the Brahmajala Sutta as quoted in this question, temporal beings who have very long lives in the Brahma realm, sometimes may think that they are the Immortal Supreme God, when that is not the case.
As described in this answer, the Acela Sutta states that the Buddha teaches neither eternalism nor annihilationism, but the middle way in terms of philosophy. Eternalism is the idea that anything (that is conditioned) can exist eternally more or less in its original form e.g. consciousness, happiness etc. Annihilationism is the idea that consciousness and existence completely vanishes at death.
Conditioning means something that is affected or influenced or conditioned by other things. For e.g. the tree grows because of sunlight, water, dropping of seed, climate etc. and does not exist as a standalone absolute entity by itself. The Buddha also said that all conditioned things are not permanent.
Now for some discussion:
The human person is conditioned, hence he does not exist eternally i.e. there is no eternal soul, but at the same time, his existence does not completely vanish, and he continues again in another birth.
The different worlds in the Buddhist cosmos are also conditioned and experience change. They too will pass away and return. In other words, there is no single point of creation and destruction for the universe. It comes and goes eternally.
Now assume that there is a Supreme Creator God. He must be a being who can observe the world, who thinks, who does things like creation and who communicates with other beings. This supreme being can be satisfied with his creation and could reward them. Or he could be unhappy with his creation and punish them. He could decide to punish, and then change his mind and grant pardon. He could communicate laws to his creation at some point, then change or update the laws later. He might want his creation to worship him and could reward them for it.
From the perspective of Buddhism, such a being displays all the marks of conditioning, hence cannot be eternal or absolute. Such a being must be within the realm of suffering just as you and I, and must at some point pass away. It is not inconceivable that there are beings with extremely long lives, who have powers and influence over other beings, but they cannot possibly be eternal, absolute or exclusively unique, according to Buddhism. Even the Buddha himself (the person who thinks and moves and communicates) had passed away.