Had something similar in my old flat in Dundee, though it was more cupboard doors drifting open rather than slamming. Less dramatic but honestly more unsettling - there's something about slow movement with no apparent cause that gets under your skin more than a bang.
The 3am timing is interesting though. You're not the first person to flag that specific window. Whether you subscribe to the ". Witching hour". Framing or prefer a more grounded explanation like barometric pressure shifts affecting door seals, it keeps coming up in these reports with suspicious consistency.
Few things worth ruling out before you go full poltergeist:
Thermal expansion - kitchens cycle between hot and cold more than most rooms, Vibration from pipes or appliances - a fridge compressor kicking in at the wrong moment can do odd things, Poorly fitted hinges - boring, but worth checking
That said, if you've already eliminated the mundane stuff, I'd want to know more. Is it always the same cabinet? Any other activity in the house - objects displaced, cold spots, that sort of thing? Pattern recognition is everything with poltergeist cases.
I've got a couple of Govee temperature and motion sensors running in rooms I'm monitoring at the moment. Might be worth setting something similar up overnight just to see what the data actually shows rather than relying on memory. Our brains are terrible witnesses at 3am.
What's the property history like?
