can I reserve later in Spain?

No, unless you want to stay in hotels, “hostals” (simple hotels)  or private "albergues" (pilgrim's hostels).
It is generally not necessary. There are many albergues, often only a short distance from one another.
Furthermore, why should you tie yourself  to a certain place? The Camino is also about: living from day-to-day and just seeing where you end up, right?
 
By the way ... we do not think it is necessary to bring your own sleeping mat. Many pilgrims apparently agree, because they leave their mats behind in our hostel smiley