And by "the board" I trust you mean the MSI PRO X670-P WIFI motherboard.
There's nothing incorrect about the behavior of the SSD when it's being operated outside the prescribed voltage and power thresholds.
If there's a trickle (and to be clear, the 5V at 300 mA available from an HDMI cable is a trickle for a full motherboard) of current into the 3V3 bus on the ATX connector, something will be the very lowest PMIC to turn on. It's just that on this system, the SSD was the first thing. If anything, the SSD will probably be highly tolerant of brownouts because its LDO will run at around 1.9V.