Without a LAN cable (and no WiFi, of course) it shouldn't be possible. Wake on LAN wakes up the computer only when a magic packet is received. No LAN cable, no packets.
There is yet another wake up mechanism in BIOS, RTC (real time clock) wake up, if that is set, then the computer will wake up at the set hour.
Other than that, it could simply be power line glitches big enough to induce current in the wires of the power button, and the glitch is interpreted by the motherboard as a power button press. Could happen if some neighbor has very noisy motors, like power tools switching on/off, maybe a refrigerator or a washing machine motor. Less common, but it can happen.