The pilot reported that after an uneventful landing, the airplane drifted approximately 20 feet to the left of the runway centerline during the landing roll on a gravel and turf runway. The pilot corrected back to the runway centerline just as the airplane’s nose landing gear dropped into a large unnoticed hole. The airplane came to an immediate stop and sustained substantial damage to the firewall. The pilot reported no mechanical failures or malfunctions prior to the accident.