Highly unlikely you’d get approved while still under your initial service obligation. Not impossible but from what I’ve seen, not likely. You’d need to be within roughly a year of your end of obligation.
You have to perform well in your current job. If you’re a turd, odds are the Marines wouldn’t want you.
The process takes awhile. My transfer to the AF took about 15 months total. Could be quicker since the Marines are under the Dept of the Navy.
That’s the NPC website. There are governing DoD instructions as well.