The best way to boost incomes at the low end is to stop illegal immigration. Workers who are here illegally will work for much less. I know from personal experience (personal knowledge of people here illegally, how they live, and the work they do).
One fallacy is that “Americans don’t want those jobs”. True, because the jobs pay so little. Eliminate the pool of workers willing to work for so little, doing unpleasant work, and guess what? The pay rate will naturally rise.
I am not saying that the minimum wage should not be raised. I am saying that illegal immigration puts enormous downward pressure on wages at the low end, dragging everyone’s pay down with it.