If the start is 2259; Pike has 7 years. Even given the fact that in TOS S1 - "The Menagerie", they state there's been Subspace chatter about the accident for months, if you go by what's currently accepted in fandom and Michael Okuda's Trek Chronology, the incident that causes Christopher Pike's injuries occurs sometime in 2266.Question: how many years does Pike have from the start of SNW before he ends up in the chair? I know very little about TOS era Trek.
That said Captain James T. Kirk is given command of the USS Enterprise sometime between 2264 and 2265. So there's that aspect to consider as well.