Unfortunately it is impossible to predict when boarding will start, unless it has actually started.

Well, technically it is possible if the staff will push a button when they are 5 min from boarding, but at AA that will never work. Indeed, with other airlines as well, their goal is to get everyone lined up and waiting at the gate whether or not boarding is really about to start. This app goes the opposite way, the tradeoff is you might board later than your early group.