Having enough saddle time in to be able to ride much of the day without discomfort is a big plus. Being a trained athlete is not a requirement though.

If you take it easy and ride at a pace and duration that is comfortable for you, in 10 days to two weeks you will likely be in the groove. Too many folks go out too fast and too far too soon and pay for it.

That said depending on where you go, distances between good places to stay and terrain may require that you ride longer and harder days right from the start. I think that on most routes that isn't a big problem. I know that on the TA we found it pretty easy to just take it easy in the beginning, but on our tour in the Sierras the difficulty of the terrain and the distance between good places to stay required hard days in the saddle (hard for me at least). I started that tour in less than great shape and paid for it, the heat was probably as big of a factor as anything though.