How long does it take for cancer to be detectable if it grows from a single cell?
The barriers you mention are outlined well in the classic Hallmarks of Cancer paper: http://www.cell.com/abstract/S0092-8674(11)00127-9

The main problem with finding a general answer to this question is the large diversity in cancers, and the resulting problem in defining what hallmarks are sufficient to call an individual cell cancerous. There are cancers that can't be detected by the immune system or blood tests and will hide for a very long time symptom-wise, and non-cancerous tumours that can be detected in various ways very early on.

Let's say for your timing reference you simply take the point of neoplasm diagnosis (for neoplasms that turn out to be cancers after testing). At this point, figuring out how much time this cancer has spent being cancerous is very difficult, and to my knowledge has never been done. It could be possible to determine:


The number of genetic or epigenetic malfunctions that made the difference between benign tumour and cancer for this particular neoplasm (once again, hard to define)
An approximate rate of acquiring those malfunctions. Conceptually, one could ex vivo culture the cancer and monitor the rate of aquisition of further mutations in cancer-related loci or epigenetic markers.


Depending on how that rate looks, it may be possible to reverse extrapolate the rate of acquisition before diagnosis, and thereby estimate an approximate timepoint of acquisition of the first proper cancerous malfunction.

Besides that, "it probably took more than a few days" is the only statement I can confidently make, although as far as biological theory goes, it's perfectly possible (though highly unlikely) for a cell to acquire a set of mutations sufficient to become cancerous in a single round of replication.