It is always hazardous to talk in broad terms of ancient Greek philosophy. In the case of the world, Plato* and Aristotle believed in the existence of a single, eternal world which none the less they conceived differently.
Anaximenes, Heracleitus, Diogenes and the Stoics appear to have believed in a continuous series of single worlds. Empedocles accepted a discontinuous series of single worlds with nothing - no kosmos - in the intervals between worlds.
Anaxagoras, Archelaus, and Metrodoros of Chios inclined to the view that there is a single world only, which came into existence with the beginning of time.
Quite a variety of views here !
As to Aristotle's view that the world is uncreated and eternal, this is a central claim of 'De Caelo' ['On the Heavens']. Aristotle's arguments may not be impressive but he does try to make a reasoned claim. It is briefly that the kosmos is too vast, complex, and tightly structured to be the work of any conceivable agent, let alone (a dig at Plato's 'Timaeus') a 'demiurge' or 'craftsman' (technites) who creates the organised world from pre-existing materials. Since no-one and nothing is a plausible creator of the kosmos, it must always have existed.
Weak as the argument may be, it is not myth or a reworking of myth but a genuine form of argument.
F.M. Crawford, 'Innumerable Worlds in Presocratic Philosophy', The Classical Quarterly, Vol. 28, No. 1 (Jan., 1934), pp. 1-16.
W.K.C. Guthrie, 'A History of Greek Philosophy', VI, Cambridge : CUP, 1981, 86. (On Aristotle.)
- I have followed Cornford here but am not wholly certain that this is Plato's view. The matter is too complex and controversial to go into here.