It is worth a shot. Normally I have only had to do it with mechanical drives, but I suppose negotiation could take longer on some SSD, too.
If you have a "quick boot" type feature in the motherboard I would try disabling that one, too.
My in laws computer I had to turn on the extended memory testing to get it to boot everytime. That's where it slowly counts all the RAM like it did on an old 486. Just those extra 10 seconds made it boot everytime, but the regular test resulted in an experience like yours.
The fact this it boots after hitting reset, seems to indicate it just needs an extra few seconds to warm up something in the system. That is my working theory anyway.