Nvidia announced a new feature designed to save you time this week - and it's already available in beta form in the Nvidia app. Auto Shader Compilation (ASC) essentially prevents your existing shader cache from being wiped after a graphics driver update, as it automatically recompiles your shaders in the background after the update is complete and while your computer is idle. It doesn't fix first time shader compilation stutters, but it may be a first step towards a wider solution there too.
Right now, ASC ought to prevent the annoying precompilation step needed when starting up a game for the first time after updating your GeForce drivers. That's particularly useful for multiplayer games that you play regularly like Fortnite, Battlefield 6 or Arc Raiders, especially if your friends are waiting for you to get online.
The same feature also prevents stutters from shaders that aren't included in that precompilation step, with the important proviso that you need to have generated those shaders manually at least once beforehand. That means "first play" stutters aren't affected by this feature, though our experimental testing does reveal some interesting routes forward.

In short, it's possible to copy shader cache files between different machines running the exact same graphics card model, thereby preventing those first play stutters on a machine that would otherwise experience them. That is probably of limited utility right now - how often will you want to play the same game on the same GPU but on different machines? - but Valve's approach with the Steam Deck is instructive. Here, shader caches are distributed automatically alongside games using a library and Vulkan layer called Fossilize, allowing Steam Deck users to have a more stutter-free experience without any special intervention.
It's easy to hypothesise about a more platform-agnostic alternative for Windows machines in the future, where shader compilation is crowd-sourced and distributed by the Nvidia app. That would take the burden off game developers, who often dedicate a lot of time to getting shader precompilation right - or suffer the consequences of a stutter-filled first playthrough.
For now though, the ASC beta is well worth enabling in the Nvidia app. After installing Game Ready Driver 595.97 or later, you can find the option in Graphics > Global Settings > Shader Cache. Here, you can enable it and choose how much of your system's resources are dedicated to recompilation. There's also a "compile now" button to get started immediately if you prefer.