There isnt. K8 does start pods and services fast. Im able to launch an entire stateful WordPress pod (multi-container) in just ~10 seconds. Including the provisioning and attaching times of PVs from scratch. This is at Digitalocean. You can easily run stateful things like WP if you build your pods well and use PVCs - even without needing to make them stateful sets. It ends up being a neatly constructed, integral VM living on virtualization. Everything is taken care by K8.
When using K8, if you use the most basic K8 features and concepts, things generally work out pretty ok.
10s isn’t terribly long but, honestly I think 1s should be achievable and would open up more use cases for K8s in general (cloud provider physical machine latency not withstanding of course).
1s is very achievable iff you have spare capacity and images already pulled. There's good reasons the latter is hard to achieved, and the former is a tradeoff few are willing to make as it increases costs.
