I don't think that even the earliest Buddhists thought of the Buddha as 'just a man'. The Pali discourses are filled with hagiographical notes, with suggestions that the Buddha was the embodiment of perfection.
https://en.wikipedia.org/wiki/Buddhahood
The Chinese are almost all Mahayana Buddhists, who believe in the existence of supermundane Buddhas.
The Mahayana Buddhists developed kind of a trinity doctrine of their own. They imagine the Buddha having three different forms.
First, there's the
Nirmanakaya. This is how the Buddha manifests as a human being on the Earthly plane. The historical Siddhartha Guatama was this Buddha's Nirmanakaya.
Second, there's the 'enjoyment body', the
Sambhogakaya. This is a glorious god-like form that the Buddha supposedly assumes when he's in the heavens among the devas.
And lastly, there's what the Buddha truly is, the
Dharmakaya. This one started out in the early Pali discourses as a description of the dependent origination, the causal process, that people confuse with a substantial mind, soul or self. But as time went on it turned into what Buddhist piety imagined as the embodiment of enlightenment itself - ineffable and without any boundaries or limits.
So from the point of view of belief in supermundane Buddhas, it makes sense to pray to a heavenly Buddha with a divine form and miraculous supernatural powers (there's supposedly many Buddhas, each spatial universe and temporal eon has one). In the Trikaya scheme, these would be Sambhogakayas.
https://en.wikipedia.org/wiki/Trikaya
Mahayana also places great emphasis on the
Bodhisattva path. This is the path that a sentient being takes towards ultimately becoming a Buddha. As time went on this Bodhisattva path was imagined as being more and more grand and elaborate, so that highly advanced beings nearing Buddhahood were heavenly beings in their own right, able and willing to answer prayers.
https://en.wikipedia.org/wiki/Bodhisattva