Pamplona to Santiago in 22 days? Definitely do-able. It depends partially on the kind of shape you are in.
However aside from your level of fitness, there are certain other considerations that might affect your desire of whether to move that quickly. Many people form little “Camino families” preferring to continue much of the journey with the same group of people. This is not likely at such a pace as not many others will keep up with you. As a consequence, in lieu of perhaps forming stronger bonds with fewer individuals you will meet a larger total number of people.
Some may argue that you will have a sense that you are in a race to get to Santiago, thereby not taking time to smell the roses. That depends on the person; for some a faster pace can actually provide a natural endorphin charge, thus enhancing the entire experience and making those roses far more vibrant.
If on a tight schedule to Santiago you find that you have a desire to slow the pace or stop somewhere for an extra period of time, there is always an option of taking some form of transportation for a stage or two. Not that this would be your intent from the outset, but knowing it is possible relieves any time pressure.
My bottom line suggestion is that if at all possible try to schedule a few more days into your trip. Even if reaching Santiago in 21 or 22 days, it’s nice to spend extra days on the back end either in Santiago greeting people you met along the way or unwinding by continuing with a walk to Finisterre. You won’t regret the additional time.
If you absolutely only have 22 days and are physically fit, planning to begin from Pamplona seems like a good idea. When you are a few days to a week into the Camino you should be in a position to judge whether you are on pace. If not look at perhaps hopping a bus for a portion of a less interesting section.
My own experience as a relatively fit 50+ year old was to have in 2010 twice completed the Camino from SSJP to Santiago. Once in 21 days, the other in 22. In both instances I allowed 33-35 days thus having no compulsion to go at any particularly fast pace. That pace was most comfortable for me and in the end that is what matters for each individual.
Buen Camino!