Had something similar in my old flat in Norwich years ago. Wasn't cabinets but the airing cupboard door would swing open around the same time every night. Took me a while to rule out the boring stuff - drafts, warped wood, the house settling. Once you eliminate all that and it's still happening, that's when it gets interesting.
The 3am thing is documented enough that I take it seriously. Whether that's because something is genuinely more active then or because thats just when the house is quietest and we finally notice it, I honestly don't know. Both feel worth investigating.
What's the build of the house? Age, location, any history you know about? And has anyone else in the property witnessed it or is it just you? Those details matter a lot before jumping to poltergeist. Not saying it isn't, just saying lets rule things out properly first.