Had something similar at my old place in Preston, cabinets in the kitchen would be wide open every morning and I lived alone. Never actually heard them slam though, just found them open. Did you set up any cameras? That'd be my first question tbh.
The 3am timing is interesting as well because that comes up a lot in poltergeist reports, some researchers think it's connected to the body being in its deepest sleep cycle and whatever is causing the activity knows it won't be interrupted. Or it could be temperature fluctuations causing wood to expand but that feels like a stretch if its happening consistently at the same time.
Has anything else been happening or is it just the cabinets? In my experience poltergeist stuff tends to escalate if you ignore it, so worth keeping a log of dates and times if you haven't already.