What time or which time?

As you noted, the word "which" when asking a question is typically used to imply a choice between definite values or a small potential list. On the other hand, "what" is used to asked for a single answer without providing options or when the set of options is large.

Keeping that in mind, there are 24 hours in a day and 60 minutes in each hour---by that count, "what time is it" has 1440 answers!

Some examples using the one object (color) that is sometimes a definite list and sometimes not:

Which color do you prefer: red or blue?

What is your favorite color?

Which of the colors of the rainbow do you like best

The last one doesn't provide an explicit list, but the rainbow is often considered to have 6-8 specific colors so the scope of the choices is still limited.

You might use "which" in association with time if you narrow down the options:

Which works best for you: 9am or 2pm?

Which do you prefer: morning or evening?

What time tomorrow works best for you? (very open-ended)

Going the opposite direction, "what is your favorite hot beverage" would be a different way to frame your first question.