Good advice, but you may be overlooking that the OP is building a Chicken Coop, rather than home. Also the desired, were to avoid the protruding window situation. JMO.
I know you said in your original post that you are a beginner at building. Everyone is a beginner at some point. I think you are doing a GREAT job at this point.:thumbsup
Consider this,,,, It is what I would do.
Remove window and cut off the inner portion of the J-channel. Insert into opening...
Uninstall your siding since that should have been the last thing to be put on.
Install your window onto your plywood sheeting. Then use a brickmold if you want. You can just install the j channel onto edge and then proceed to put up the siding. You only need to remove the siding as far down as...