There are two peak arrival surges each day at the Pilgrim Office. The first daily surge is from 10:00 until about 11:30. The second surge is from about 1:15 (directly after the noon Pilgrim Mass lets out) until the resulting longer queue is processed. However the size of these surges is relative to the time of year.
Generally, there is a surge of arriving pilgrims each morning about 10:00 - 11:00 as newly arriving pilgrims in Santiago proceed directly to the Pilgrim Office, assuming they can easily obtain their Compostelas, find a place to consign their rucksacks (as rucksacks are NOT permitted in the Cathedral for obvious security reasons), and make it to that days' noon Pilgrim Mass.
This MAY be possible in the off-season, before or after the period between the end of September and Easter. Once Easter arrives, the peak pilgrim arrival season begins. Each day, until the end of the following September, the "easy-peasy" process no longer applies. Each day gets busier and busier, with a spike coming once schools are out for the summer holidays across Europe.
The annual surge does not begin to abate until after the Festa de Santiago on 25 July, and the customary August holiday season for many European residents. Only once the schools are all back in session in September, do the daily volumes fall into the off-season pattern.
Walking into Santiago, proceeding to the Pilgrim Office, consigning one's bag and attending that day's Pilgrim Mass is generally NOT readily doable if you arrive at the Pilgrim Office after about 09:30 during the peak season. That was the fact during July and August when I worked there this summer, and last summer, and the summer before that...
This year, I actually had pilgrims get angry because they could not walk in from Lavacolla arrive at 11:00, obtain their Compostelas, consign their bags, attend the 12:00 Mass, see the Botafumeiro, AND then make their 14:00 bus departing Santiago. These folks thought it was somehow, MY fault, or the fault of the 13 workers and volunteers working assiduously to process as many Compostelas as humanly possible.
Once the noon Mass is over there is a second, literal wave of pilgrims descending on the Pilgrim Office. One can actually watch them "roll" down Rua das Carretas towards the Pilgrim Office. One of my lesser functions each day was to walk into the processing office and alert the staff that the post-Mass wave was clearly coming down the street.
"All-hands" were summoned from breaks, lunch, or collateral duty to return to Compostela processing. Additional volunteers were requested from logical seminaries. These folks take this job VERY seriously. Without the added volunteers, the daily lines would have been many hours long.
My advice to all pilgrims arriving at any time of year, is to allow adequate time for what your priorities are. The Pilgrim Office has long hours, seven days a week, 363 days per year. The are closed ONLY on Christmas Day and New Years Day. I advise taking care of your personal arrival ritual at the Cathedral FIRST. Consign your rucksack somewhere for the day, get to the Cathedral, attend the noon Pilgrim Mass. After the Mass, check into your lodgings, store your rucksack, have lunch. There is plenty of time to get to the Pilgrim Office when there are short to nil lines.
Even during the busiest days this past summer, each day about 5:30 - 7:30 each evening, there was usually virtually no line. Even if there was a short line, a pilgrim could be in and out in 15 - 20 minutes.
Knowing the office closes at a certain announced time. there is a final, end of day surge of pilgrims trying to obtain their Compostelas before the office closes. Security personnel will close the outer access doors and gate 30 minutes before closing time. All pilgrims inside when this happens WILL BE PROCESSED.
The biggest problem is unrealistic expectations among arriving pilgrims. I always advise taking care of everything EXCEPT the Compostela on your arrival day. The Pilgrim Office has been there for years, is not going away, and the supply of blank Compostelas will surely not run out. Come to the Pilgrim Office early the following morning, before the "10:00 crowd" walks into town. You will be in and out surprisingly fast.
I hope this helps.