I can think of a few ways increasing minimum wages might increase employment at least for small enough increases (for large enough increases, no one can hire you):
Market wages may be below wages that maximize productivity/efficiency, since increasing wages increases productivity. Setting higher wages could therefore in principle allow a company to hire more people. See efficiency wages. I think companies by default will pay low-skilled workers as little as possible, not knowing they can do better by increasing wages, so it wouldn’t be too surprising if increasing the minimum wage sometimes increased employment. Walmart has been voluntarily increasing wages, and it might be good policy. Of course, a minimum wage is a pretty one-size-fits all, and it might be too high for some companies and too low for others.
I can think of a few ways increasing minimum wages might increase employment at least for small enough increases (for large enough increases, no one can hire you):
Market wages may be below wages that maximize productivity/efficiency, since increasing wages increases productivity. Setting higher wages could therefore in principle allow a company to hire more people. See efficiency wages. I think companies by default will pay low-skilled workers as little as possible, not knowing they can do better by increasing wages, so it wouldn’t be too surprising if increasing the minimum wage sometimes increased employment. Walmart has been voluntarily increasing wages, and it might be good policy. Of course, a minimum wage is a pretty one-size-fits all, and it might be too high for some companies and too low for others.
Increasing the minimum wage may reduce burdens to a community from suicide and substance abuse. I would guess that if someone in your family commits suicide or uses drugs, this has a negative impact on your own employment prospects. The effect on suicide rates seemed pretty small, though.