Nvidia has provided a new GPU firmware update for the RTX 3060 and RTX 3080 TI that fixes black screens on boot with DisplayID monitors running on a DisplayPort connection. Nvidia's GPU Firmware Update Tool can be found here (opens in new tab).
DisplayID is a relatively old technology, first introduced in 2009, that allows a computer's GPU to see all the capabilities of the display device, like G-Sync support or FreeSync support, for instance. The latest version of Display ID, version 2.0, came out in 2017 and added support for 4k and higher resolutions, HDR, VR, and 120Hz support and above.
If you have any modern DisplayPort monitor, it is almost guaranteed to have DisplayID built-in as it is necessary for the GPU to see the monitor's features and enable them, like high refresh rates and HDR. Unfortunately, some displays have been having compatibility issues with certain Ampere GPUs, resulting in a black screen. This update should fix that.
Of course, if you're currently having this black screen problem, running the tool may be difficult. Nvidia recommends using a different display source, such as HDMI or DVI, or some other method of display output, whether it be from another GPU or monitor.
Once you run the tool, it will automatically detect if the firmware update is needed and install it if you have the DisplayID issues. Nvidia recommends that you do not update your GPUs firmware with this tool if you do not have the issue.
For now, it appears the problems largely impact the RTX 3060 and RTX 3080 Ti, according to Nvidia. However, the firmware update can be applied to all RTX 30-series products if necessary.