Mate this is genuinely weird because I had the exact same thing happen during a session I did last year in an old chapel outside Cardiff. Three recordings, three separate nights, and every single time there's this burst of static that shows up right around 3am on the waveform. Not near 3am, bang on it.
I've heard the whole "3am is the witching hour, opposite of 3pm" thing and I'm usually pretty sceptical of that kind of lore but its hard to dismiss when you're staring at the timestamps yourself.
What equipment are you using? I was on a Zoom H5 and at first I thought it was interference from my phone but I'd switched it to airplane mode so that rules that out. The static isn't random either, it has this rhythm to it almost like its trying to be something. Never managed to clean it up enough to make out anything clear though.
Would genuinely love to compare raw audio files if anyone's up for it. Crowdsourcing this kind of thing is way more useful than everyone sitting on their recordings alone.