I'm not an expert but I have some background. The single cell that eventually becomes the cancer has to meet a few criteria. There are genes that can be activated which constantly keep the cell growing and dividing due to a mutation in that gene or genes that code proteins that are supposed to repress it, instead of dividing a set number of times and periodically as is normal for most cells. There are also checkpoints that keep cells that are not ready to divide or are too rapidly dividing from moving onto the next step in the cell cycle, and the genes controlling this part can be mutated as well. There are a bunch of different genes that can lead to cancer if they get damaged or over expressed, but in most cancer cells more than one gene is abnormal. Our evolution has tried to protect us from cancer in many many ways. You could genetically or environmentally have one or two messed up genes and then you might be predisposed to or "almost" have cancer because something could come along, mess up another gene that was preventing the cancer, and become cancer.

Or if you look at the question differently, you could have a tumor that is not yet cancerous. A polyp in your colon could be "almost" cancer. It has to progress and invade other tissue I believe is the criteria for being actual cancer, either by metastasizing or invading surrounding tissues. I am not sure if this part is accurate, but I thought that was what distinguishes between a benign tumor and cancer. Keep in mind that the term cancer covers a number of different diseases so if we know a tumor is likely to spread, we may still call it cancer, and there are a ton of tumors not capable of invading tissue.