There must have always been a relatively large number of people who appeard to suddenly become very ill then die, so what did people think was happening? Do we know of any civilizations attempting to treat cancer? Are there ancient sicknesses that we now know were cancer?
Hippocrates knew about cancer (and is the person who named it), so it was known by around 400 BCE. When cancer gets advanced enough, the tumors are visible and you don't need any particularly sophisticated medical technology to see that they're making someone sick.
Cancer correlates closely with age. As people died much younger cancer was rarer. However the illness was observed. Hippocrates says that Atossa the queen Persian (Cyrus' wife) of has a (vulval?) tumour excised by a slave named Democletes ; this according to Herodotus is a causal event of the Persian wars.
All accurate information below is from my memory of the book the Emporer of Maladies by Siddartha Mukherjee the errors are mine.
Imhotep described breast cancer as a cool mass "dense as a hemat fruit" for which there is no cure.
Galen claimed cancer was caused by 'black bile' (a choleric humour) as such it was not treated by excision until the 19th century. It was believed that surgery would only treat a symptom and that excising a tumour would not cure the disease. Surgeons actively refused to excise.
This black bile theory was disproved by Vesalius in the 16th century but sort of hushed up. (He found some other humours blood and lymphatic fluid anyway)
There were many means used to treat it most of which seemed to me to be magical. Prayers , arsenic, dogs bones, wormwood etc.
Excision becomes common in the late 18th century.
The 16th century novel Romance of the Three Kingdoms, set in the 3rd century, features a story you might be interested in. The warlord Cao Cao was dying and called for the finest physician around for help. The doctor tells Cao Cao that he has brain cancer and wants to treat it by removing the tumor. Cao Cao, outraged, declares that anyone who wants to crack his ruler's skull open and remove part of his ruler's brain is an assassin and declares he'd rather die of the tumor than submit to such an obvious assassination attempt. He jails the doctor and promptly dies of brain cancer.
I relay this story not because of it's historical accuracy regarding the 3rd century warlord Cao Cao, but because I think it captures the attitude towards cancer in 16th century China when Luo Guanzhong wrote the book.