As the question suggests, I wanted to ask if there really was some commoner like Shin in Kingdom who became one of the greatest generals of Qin Dynasty in reality or according to the Warring States-era history?
Yes he was. He was based off Li Xin.
Here is a great resource describing many of the similarities / differences: link
It is true that Shin is based on a real-life historical figure by the name of Li Xin. But he wasn't a commoner. In fact, he was actually the son of the governor of the Nanjun Commandery.
And about him being one of the greatest Qin generals, he certainly was a prominent general. He was one of the generals who played a very crucial role in the unification of China.