With new baby chicks, sometimes it's anyone's guess as to how they manage to get themselves into trouble at such a short time out of their egg. It's obviously a crushing injury it got somehow. Chicks are geniuses at finding ways to injure and kill themselves with very little in the way of dangerous surroundings contributing.
You can do nothing further to help the toe. It's an immune response chickens have when an extremity is severely injured. I watched over a period of time a hen I had with an injured toe go through the stages of first walling off the injury with swelling of her tissue, which cut off the blood flow, and then the toe got black, then dried out and then fell off.
After the toe falls off, the swelling of the remaining toe gradually goes away. Chickens do just splendidly with a missing toe.