When did the disease of cancer started to be recognized as such? Did cancer always exist in humans?
It’s clearly always existed in humans (and all other animals), though I can’t really cite that.
It’s been known for thousands of years. (Short version of the salient details from that link - mention of cancer treatment is found in Egyptian records from circa 1600BC, and the words ‘cancer’ and ‘carcinoma’ come from Hippocrates and Celcus, both of whom lived before Christ.)
Hippocrates called it cancer (meaning “crab”) because the tumors he saw often had long branching projections that looked to him like the claws of a crab.
Incidentally, John Adams’ daughter had breast cancer, had the lump removed, and lived for many more years before eventually dying of a recurrence.
This slightly relevant trivia brought to you by the letter “C”.
To be a bit more accurate, being Greek, he called it (or, rather, the tumors) Carcinos (Crab), which he later altered into Carcinoma (Crab-swelling). It was Celcus who later translated the name into Latin as ‘Cancer’.
Fair 'nuff
Just chiming in with some related questions:
Words for ‘cancer’ in other languages
An early theory on the metastatic nature of cancerous tumors
If only this were true.
John Adam’s daughter Abigail “Nabby” Adams Smith, was diagnosed with breast cancer in 1811. She had surgery to remove the tumor a few months later (the gruesome details of which can be found in this essay), took months to recover from the surgery, but less than a year after recovering from the surgery she exhibited signs of metastasized tumors all through her body. She died painfully in 1813. 
Hrm. Must have misremembered the details from that Adams biography I read.
As the Wikipedia notes, the confusion probably stems from the depiction of the surgery in the HBO miniseries John Adams.
A depiction that is simultaneously not that graphic, yet one of the most horrifying things I’ve ever seen.