When a question is closed, keep in mind that closure doesn't not always mean the end of a question.
We are also limited with our close reasons. Often, a question needs to be closed, but the stock choices aren't perfect matches. For your current question, that is the case.
Personally, I would have closed this question with the Needs details or clarity or Needs more focus reason. Let's dissect your original:
I would like to use drush site-install to automate installing and configuring a new Drupal 8 website. What process would I need to do to write the configuration, then perform the automated installation?
Are you cloning a site? Deploying a local one? Starting a new site from a template site? Or do you want to make a new site and fully configure it without the UI? Isn't really clear what you are after.
I looked at another answer (Installing a site from existing configuration) but it doesn't specify how you actually get the configuration in the first place, or how you pass that configuration to the install command.
Again, it isn't clear what you are trying to accomplish here.
You then made an edit to add
I've looked at creating a new, blank website, and then importing the configuration. However it doesn't seem to be officially supported, and seems difficult to automate (you have to edit a YAML file). It seems to me like this should be possible to do with a single drush command (or comparable tool).
You add what you think doesn't work, what you think should be a solution (which may or not be correct), but still haven't described what you are trying to accomplish. There are several different ways to accomplish automated installation, and some are best (or only appropriate) for certain situations.
So, I suggest editing the question to
- outline your starting point and end goal (see my commentary about the first paragraph), and disambiguate whether you have config already or don't (there are some potential contradictions in the question and the comments)
- outline what you have tried so far
From there, we can see if we can help solve your problem.