This varies wildly depending on the type of trauma, location of damage, and the mechanism, how and what kind of damage occurred.

"Coma" is actually an annoying term, largely because it's super non-specific. It can range from completely unresponsive and brain-dead with few if any central nervous system brain functions and full life support requirements, to persistent vegetative state, where someone may open their eyes, breathe on their own, have reflexes, but otherwise never interact or have meaningful expressions.

"Waking up" is also not a super explicit term, either, because plenty of people open their eyes and are "awake", but after massive brain injuries and trauma, many never recover meaningful function, and simply have reflexive movements, don't track or respond to stimulus properly, etc. Are they truly "awake", or do their eyes just open?

We generally can give people a decent idea of what kind of function to expect after trauma-related swelling, inflammation, blood collection, etc., has receded and resolved, but that can take weeks to months, dependent on the injury. Running various tests like MRIs and CTs to see blood flow to the brain and areas of injury like infarcts or mechanical changes can give us better ideas of the extent of damage, but again, time can change some things and give better pictures.

Very obvious traumas we usually know within a few weeks whether someone will wake up, less time if other organs are involved and/or failing. Less obvious or extensive traumas.. Well, months, sometimes, and even then, the results are mixed, and some "wake-up" more so than others.