"Get up as early as possible on Monday, please."

Well, it is fuzzy, so we accept a range of answers. Such usage is popular in spoken language, and means that a person wants you to get up "kind of early", "earlier than you normally would". Technically saying "earlier" implies that you compare it to something that is just "early".

Раньше is not used in that meaning (you use it to say "before", though). However, the spoken пораньше does get used to extend the meaning or "earlier" a tad bit: with this word, you can say "somewhat earlier" without specifying any reference point.

So "a little earlier", "early" and "as early as you can" are all quite valid because English does not really have a matching expression to refer to an unspecified "earlier" time, which is pretty vague but still substantially earlier than normally. A request like the one in the title typically means that a person wants you to do something come Monday, that requires you to be somewhere earlier than usual, and that means you'd have to get up earlier to achieve that. Maybe you'll have to devote quite a bit of time to that activity, so you'd want to make sure you have enough time to spare before work/school.