While DLSS has been technically available in the NVIDIA drivers for Linux for some time now, the missing piece was support for Proton which will be landing tomorrow - June 22.
In one of their GeForce blog posts, they made it very clear:
Today we’re announcing DLSS is coming to Facepunch Studios’ massively popular multiplayer survival game, Rust, on July 1st, and is available now in Necromunda: Hired Gun and Chernobylite. Tomorrow, with a Linux graphics driver update, we’ll also be adding support for Vulkan API DLSS games on Proton.
This was revealed originally on June 1 along with the GeForce RTX 3080 Ti and GeForce RTX 3070 Ti announcements. At least now we have a date for part of this extra support for Linux and DLSS. This, as stated, will be limited to games that natively use Vulkan as their graphics API which will be a short list including DOOM Eternal, No Man’s Sky, and Wolfenstein: Youngblood. Support for running Windows games that use DirectX with DLSS in Proton will arrive "this Fall".
With that in mind then, it's likely we'll see the 470 driver land tomorrow, that is unless NVIDIA have a smaller driver coming first with this added in. We're excited for the 470 driver as a whole, since that will include support for async reprojection to help VR on Linux and hardware accelerated GL and Vulkan rendering with Xwayland.