its possible there is a setting in the Toshiba bios in its boot settings where it can swap between boot methods at startup, and your hdd isn't always responding at startup so it tries the different method and you get stuck on the black screen.
2 boot methods - CSM (Legacy) and UEFI
CSM (Legacy) matches MBR drive format (what you have)
UEFI matches GPT drive format
restarting the PC makes it swap to the right one
I remember from the few Toshiba laptops I have had to help fix in last 4 years, that they use CSM mode to install win 10, so bios can use both as if it was just an old legacy bios, it wouldn't have CSM mode (there used to only be 1 boot method, UEFI was designed to replace legacy 10 years ago)
you might want to run
hdtune on the drive and check its health tab
I could be wrong, but I would think that if it was GPU drivers it would happen every startup and not be so easy to fix