Nvidia has released a firmware update for the RTX 3080 Ti, and the RTX 3060, one that addresses a problem with the screen blanking when using DisplayPort. Currently, the screen will only turn on once your OS loads, which makes getting into the BIOS problematic. Given the need for users to get into the BIOS to turn on TPM options in preparation for Windows 11, this is obviously a timely fix.
The issue is related to the DisplayID specification and will only surface if your monitor also uses DisplayID. It only affects the two 30-series cards mentioned, as well.
Nvidia says only those experiencing screen blanks should apply the firmware update. The update will check whether the update is needed, and will only give you the option of updating it if this is the case. You can grab the firmware update from this Nvidia support page.
Alternatively, if you are experiencing this problem, Nvidia recommends either using DVI or HDMI, booting using a different monitor, or using a different graphics card or the one that's integrated into your CPU—although not all CPUs have integrated GPUs these days, particularly on AMD's side.
Another of its recommendations is to switch from using UEFI to Legacy mode in the BIOS, although, in order to switch that over, you'd need to get into the BIOS in the first place. UEFI is also a better system for modern computers, so this isn't ideal on many levels.
Still, unless you've got a pile of monitors, cables, and different graphics cards to hand, this could be your only option.