how do I specify a render cache context as universal? I want to a render array in my page to be cached, and I know that it's the same for every user in every circumstance.
How do I specify that its cache context is universal, rather than anything else?
There is no universal cache context. This is the default for a render array if you don't specify any cache context.
Render contexts are merged upstream. Additionally you can configure required cache contexts which are added to all render arrays before they are rendered.
Out of the box Drupal requires these three contexts:
core.services.yml
parameters:
  renderer.config:
    required_cache_contexts: ['languages:language_interface', 'theme', 'user.permissions']

You can override the parameter in /sites/default/services.yml (use default.services.yml as template).