I don't think you can use Tasker to press the button. The reason Chromecast won't start casting without pressing something is that it's written to be used on more than one Chromecast dongle in a home, and there's no code to change that if you have only 1. (If you have 2, the choice would be cast to the first one or cast to the last one you were casting to - either of which may be wrong, and interrupt someone's TV watching at a crucial moment in the show.)