I turn my computer on, select my linux harddrive, and then I end up at the Linux mint encryption password area. I have to wait about 1 minute just for my keyboard and mouse to actually light up and become responsive. They do eventually turn on and become usable. I have a steelseries apex keyboard and anker ds-2368.
This does not happen when I boot into my Windows 8.1 drive.
Also, my keyboard and mouse initially work right after system power is one, and the BIOS / Boot menus.