I think it is inaccurate to say that Hinduism has no starting point--it has several. You can look at the birth of modern Hindutva, the British racial policies, the growth of bhakti in the "medieval" period, etc. Thinking in these terms, Siddartha was living in one of the many periods of change that wracked the religion that can be called Hinduism. More concretely, the broad historical period in which Siddartha lived (the growth of states along the Ganges) was one of crisis for the so called "Vedic brahmanism" that was he dominant form of, at least, elite spirituality in the north Indian plains. This was driven at least in part sramana religion, which were a collection of different spiritual movements that took the basic principles of the Vedas as a base but emphasized physical and spiritual purity and individual spiritual attainment. These included movements that can be considered nastika (heterodox) like Jainism or astika (orthodox) such as Vedanta. Buddhism was one of the former, heterodox schools, although it eventually became the most important religious movements in India for several centuries before its ideas were absorbed by more orthodox schools.

So I think rather than whether or not Siddartha Gautema was a Hindu, the better way of thinking about the matter is that he was a very important part of the religious movements that came to define what Hindu is.

Romilia Thapar's The Penguin History of Early India is the best widely available source on the topic 9and many more!).