I see from another thread that you are planning to start in SJPP around May 1. Here is
another thread discussing the numbers starting in SJPP, by week through the year. The first week of May is likely to be the second busiest week of the year (September has a busier week).
The highest
arrivals in Santiago are usually in July and August due to the large number of Spaniards who walk the last 100 km during summer breaks.
The first few days out of SJPP can be quite a bottleneck in May and September, because of the surge of walkers from SJPP and the limits on beds (exacerbated by Covid). This eases somewhat after Pamplona.
I would encourage you to do whatever suits you - making reservations or not. But I would not consider is a reasonable
assumption that you can walk into Roncesvalles or Zubiri and have much choice in accommodation in the first week of May.