Can increased employment follow an increase in the minimum wage?
Sure it can.
All that is necessary is that you start with a shortage of labor.
Of course, if firms respond to shortages of labor by raising wages and hiring more workers, then employment is less than it would have been if the minimum wage hadn't been increased.
And a decrease in the minimum wage could still result in increased employment as well.
Why was the market wage rate at the first minimum wage when there was a shortage of labor? Why hadn't it already risen to the equilibrium? Presumably, it was because the demand for labor had increased, and the slow and clunky market process of firms adjusting wages upward was incomplete.
There is an entire range of increases in the minimum wage that would lead to increased employment compared to where it was before an increase in the demand for labor. There are also any number of even higher minimum wages that would result in less employment.
If there were currently a shortage of labor, then it is highly unlikely that reducing the minimum wage would increase employment. On the other hand, I think it is unlikely that it would decrease employment. Just because firms are slow to raise wages in the face of labor shortages doesn't mean that they will lower wages despite shortages of labor.
And, of course, with the unemployment rate being 10%, and 57% among black men between 16 and 19, I don't think a shortage of labor is relevant to today's situation.