I haven't read the Veda or Upanishad (and other Hindu scriptures). But I'm eager to know whether it does offer any account of how the universe came into existence?
The Rig Veda 10.129 (via Wikipedia):
Neither being (sat) nor non-being was as yet. What was concealed? And where? And in whose protection?…Who really knows? Who can declare it? When was it born, and when came this creation? The devas were born later than this world's creation, so who knows from where it came into existence? None can know from where creation has arisen, and whether he has or has not produced it. He who surveys it in the highest heavens, He alone knows-or perhaps does not know.
A good place to start is Madeleine Biardeau's chapter "Vedic Cosmogony" in White's Mythology (vol. 2), 1991. Here's the Oxford Bibliography note on it:
Takes most Rig Vedic cosmogonies to be fragmentary or allusive, with two exceptions: the Indra myth, later modified due to Indra’s changing rapport with Vishnu; and the Puruṣasūkta. Only the latter, according to Biardeau, has lasting impact in constituting an order of the world based on sacrificial activity that “would come to be called dharma.”
The Upanishads by contrast moved to Brahmanic omnipotence. Alf Hiltebeitel summarizes the movement as such:
New Upanishadic teachings about the ultimacy of the self (atman) and its oneness with the absolute, or Brahman, reshape late Vedic discourses about cosmogony. If the self is all, how did it become all? Some cosmogonic passages pose that question in the name of Prajāpati, others in the name of Brahman or Puruṣa. There are also shorter passages that relate atman to cosmogonic concepts.
One book and one article you may want to check out (with corresponding Oxford Bibliography annotations on them):
Deussen, Paul. The Philosophy of the Upanishads. New York: Dover, 1966.
The classic study of Upanishadic thought, presenting it as moving toward system: particularly Advaita Vedanta. Deussen coins the term “cosmogonism” here to describe the move from stating the atman-universe identity in early Upanishads to that of stating the atman to be the cause that produces the universe. He sees this as allowing both reversion to Vedic cosmogonies and opening new theistic and evolutionistic trends. Originally published in 1906.
Buitenen, J. A. B. van. “The Large Ātman.” History of Religions 4.1 (1964): 103–114.
A landmark study that addresses many issues raised by Deussen, with supple argumentation. Van Buitenen notes consistencies across early Upanishads of an innovative cosmogony in which “the great ātman” becomes the “whole,” pervading the cosmic body and social order it creates “down to the nail-tops.” In later Upanishads and philosophical portions of the Mahābhārata, the concept becomes serialized in hierarchically scaled accounts of creation, in some of which the creator is personalized.