Is there a minimum amount of time that has to elapse from the end of the gap analysis or SCAMPI C until the initiation of the SCAMPI A? In other words, for processes not in place during the gap analysis how long do we to have them in place before starting the SCAMPI A Appraisal?
As the SEI likes to say to almost any question, it depends.
There is no rule or guideline within the CMMI that prescribes a waiting period. You could do it the next day if the results of your SCAMPI C are strong enough. However, if you've decided to conduct a SCAMPI C first, I'm thinking that maybe you don't think that's likely to be the case.
So given that, you'll need to give your processes and projects using them enough "bake time" to sensibly adopt the process and to see the results of running several projects through the "cycle." Depending on your typical project size and duration, this could take some time - say a minimum of six months to a maximum of twenty-four or more.
Like they say, it depends.