Why chemical origin of life is part of evolutionary history of the earth? Any proof of this? How is it possible that origin of the life is based on inorganic matter?

There is no proof that there is any chemical origin to life or to evolutionary history. Abiogenesis is the wishful speculation of naturalism, which holds exclusively to purely physical processes in the origin of life. The chemical evolution proposed is a myth, like Darwin's "warm little ponds" and Oparin-Haldane primordial soup.

There are no natural processes capable of abiotic elemental assembly into complex molecules that can combine into increasingly more complex levels that lead to metabolic and reproductive functions of a living entity.

Of course, all life is based on matter, there are approx 22 elements found in living entities, but their specific and precise collection and assembly is far beyond anything that the four fundamental forces are capable of processing. Of course living entities are comprised of organic matter primarily, so inorganic matter is not a consideration.

The second law of thermodynamics, the law of entropy, allows elemental assembly of inorganic and organic elements. Examples of these are amino acids, sugars, methane, formaldehyde and other simple molecules. None are strategic to the origin of life, and the full complement of required molecules far exceeds anything naturalistically possible.

Thus, it is not possible that the origin of life is based on inorganic matter.

There isnt really a actual specific origin, although from the big bang and atoms, etc. also by knowledge of the evolution process.