This is one of the things we (at https://fal.ai) working very hard to solve. Because of ML workloads and their multiple GB environments (torch, all those cuda/cudnn libraries, and anything else they pull) it is a real challange just to get the container to start in a reasonable time frame. We had to write our own shared Python virtual environment runtime using SquashFS distributed thru a peer-to-peer caching system to bring it down sub-second mark.
After the container boots, there is the aspect of storing model weights, which IMHO less challenging since it is just big blobs of data (compared to Python environments where there are thousands of smaller files where each might be sequentially read and incur a really major latency penalty). Distributing them once we had the system above was super easy since just like squashfs'd virtual environments, they are immutable data blobs.
We are also starting to play with GPUDirect on some of our bare metal clusters and hopefully planning to expose it to our customers, which is especially important if your models is 40GB or higher. At that point, you are technically operating at the PCIE/SXM speeds which is ~2-3 seconds for a model of that size.