Had something similar in an old terraced house in Rugeley back in 2009. Three cabinets in the kitchen, not just one, all on the same wall. The pattern was what got me - always between 2:50 and 3:15, never outside that window. Classic infrasound territory honestly, a specific frequency can physically vibrate cabinet latches open if the conditions are right, but that doesn't explain the audible bang each time or why it stopped completely after about six weeks and never came back.
The 3am thing keeps coming up with poltergeist reports and I'm not entirely sure what to make of it. Some researchers link it to cortisol dips in the human body affecting perception, others go straight for the "witching hour" angle which I find a bit theatrical.
What's your house history? Age of the build, any major works done recently, anyone in the household going through a stressful period? Poltergeist activity correlates strongly with stress in the occupants, thats well documented across the literature. Would help narrow it down a bit.