The granting of Major Works Licences depends on the local council. In my experience they are usually granted in 4 to 12 weeks, although in Madrid, for example, it can take up to 12 months. Having said that, some Councils will allow you to start work whilst the Licence is being considered when the works are to an existing building, although obviously anything you do will be at your own risk.
The most important piece of paperwork is the “Asume de Dirección”, which means that the Architect has informed the Council that he or she will be supervising the works, and therefore taking legal responsability for them. The “Asume” is issued by the local Architects Institute to the Council, and make sure that you have a copy of it before anybody starts work.