You could probably get close by auto-deploying from GitHub Actions but you wouldn't get the main benefit of a service like that (having ops done in a clean way without having to think much about it).
Without having any experience in the field, aren't lambda functions supposed to provide something like that?
Ideally this would be a service with the same ergonomics but the outcome isn't a hosted static website but a machine (somewhere in the cloud) running whatever the user wants. "Tedious" tasks like hardening, monitoring and upgrading (and redeploys) would be handled by the service provider, as opposed to the user.
For people who like doing ops this might not sound appealing but developers (especially single devs and small teams) often just wanna focus on their app, not their ops, even more so when it comes to continous maintenance.
Addendum: I think Laravel has some of this covered in their ecosystem with tools like Forge and Envoyer. But I've never tried any of them so I can't judge.
Since then we've seen "serverless" or functions-as-a-service (FAAS) which is just smaller bits of code (down to a single javascript function) but the same concept of everything else being managed by the provider. This is AWS Lambda, Cloudflare Workers, Google Cloud Functions, etc.
The latest offerings now take a Dockerfile or container image that you build, which means you can run anything on any stack while the provider manages the rest. Google Cloud Run, AWS Fargate, Azure Container Instances, Fly.io, Zeit Now, etc.