Consider that it takes three, full days walking to arrive at Pamplona from St. Jean Pied de Port. Add an extra day if you plan to stay at Refuge Orisson on the first night.
Work backwards from when you DO NOT want to be at Pamplona, or any similarly large town or city along the Camino, where waves of new pilgrims will join the Camino. These "new starters" usually start mostly on Saturday and Sunday mornings. So you want to be gone by Friday, or arrive on Sunday to leave on Monday.
Hence, the new pilgrims will likely arrive at their starting place (Pamplona, Logrono, Burgos, etc.) on Friday or Saturday evening. Accordingly, they will stress available reservable bed space on Friday and Saturday nights more than any other night. These cities and large towns have good rail and bus connections to the rest of Spain, and onwards to the rest of Europe.
Logically, you want to get in and out of these starting nodes by Friday or arrive on Sunday or Monday. This puts the wave in front of you.
Bottom line, and to answer your original question directly, I would start on a Monday,stay at Orisson the first night and arrive at Pamplona on Thursday afternoon. This puts you down the road from Pamplona on Friday, and one to two days in front of the coming wave.
Finally, use this "model" for your entire Camino if you want to avoid the congestion that the infusion of weekly "pigs in the hose" can produce. If you make advance reservations at private albergues or hostals, a smart phone, or web capable device that can use the ubiquitous Wi-Fi available at most cafes and overnight accommodations will help.
There are many online reservations choices. I have always had good luck on the
Camino Frances with
www.booking.com. They also show a lot of private albergues. They do not feature public albergues asa they are not reservable. To find these, try the many online app guides, or go to
www.gronze.es.
I hope this helps.