There's no harm in writing to companies you'd like to work for and starting get your name known at early stage in your training - in fact that's a very sensible and positive thing to do.
However you can't make a serious "application" until you have all the ticks in all the boxes. You will probably not get a SIM ride before you pass your IR!
Al
P.S. I have put the word application in inverted commas as there really is no such thing in this industry - most of the time you will be sending out speculative CVs and hoping that the powers that be like the look or sound of you. I'm not trying to be cynical or put you down, that's just the way things are!