Let's just assume for the sake of it that it is what you call a 'zero sum game', although it clearly is not.
I said that, so long as we emphasize economic growth, the immigrant and the native-born can each find jobs. That is, it is NOT a zero sum game.
Those who came here with their parents are the subject of this thread; you seek to demonize then as "illegals", but these folks are without moral fault. The idea is to normalize their status so they don't have to compete unfairly with citizens in an underground economy. They pay the same taxes and face the same obstacles to getting a legal job as anyone else - that is, they must compete, and win, fair and square. And many of them, it appears, are doing well, because they have the drive and ambition that too many native-born lack. Let's not forget that employers like immigrant labor, not because it's cheaper and easier to exploit, but because it shows up to work on time and is willing to go where the opportunity is.