Personally I would make a reservation for that first night.
You'll be arriving in town after most walking pilgrims so many albergues may already be full, and - it's Sarria, where many others like yourself start their Camino, and may well have made reservations, or have arrived in town before you. September is a busy month.
I can't suggest any pensions in Sarria (I stayed at Albergue Don Alvaro), and on another trip I stayed at Pension 108 to Santiago in Barbadelo (4km from Sarria along the Camino) and that was very nice, it's right next to Casa Barbadelo which also has private rooms. Anywhere more than 100km from Santiago still counts for the compostela, so it's a perfectly legitimate starting place.
It will still be light in the evenings, so you could always walk those first few km there, and get a head start in the morning!