Shiva has no single point of origin that scholarship can identify, and the honest account of where he comes from is an account of several unresolved arguments.
The clearest thread is Rudra. The Rigveda gives Rudra only three of its one thousand and twenty-eight hymns, and treats him with an anxiety it uses for no other god: he is asked to spare people, cattle and horses, to strike somewhere else, and he is called shiva, kindly, in what reads plainly as placation rather than description. The Shatarudriya of the Yajurveda salutes him in a hundred aspects, including thieves, hunters and men of the wilderness, and the Shvetashvatara Upanishad takes the further step of treating him as the single god behind everything. That is a traceable line from a marginal Vedic figure to a supreme one.
The other claimed thread is not traceable. In 1928, and at greater length in 1931, John Marshall identified a seated horned figure on a seal from Mohenjo-daro as a prototype of Shiva, on four grounds: three faces, horns, a posture he read as yogic, and surrounding animals matching Shiva's epithet Pashupati, lord of animals. The identification entered popular writing and has stayed there. It has not held up well. Herbert Sullivan questioned the male reading in 1964. Doris Srinivasan argued that the lateral projections are bovine ears rather than faces and that the figure is better read as a divine buffalo-man. Asko Parpola compared the pose to Proto-Elamite seated bulls. Gregory Possehl accepted a deity in a ritual posture but held that calling it proto-Shiva goes too far, and Wendy Doniger has written that whatever the resemblances, we cannot know.
The Indus script is undeciphered. Until it is read, no religious identification of any Indus image can be more than a proposal, and this atlas states Marshall's claim as his and not as fact.