Baby fish start out a color called "green" - a kind of gray. They will then "de-color" or get their first colors as they age. Calicos and some soft gilled whites will de-color first - so when they are about 1/2 inch or so on many breeds you will begin to see calico fish in the group. Others take longer to take on adult coloration.
Blue fish seem to wait a LONG time to get their true colors - up to a year or more.
A young fish will often have large spots of black or dark brown on them. As they age, the black is commonly replaced with red/orange colors. Calicos typically stay calico, but the other fish that appear to be "dark" will commonly change to reds as they reach 1-2 inches.
You can often find young fish (under 3 inches) that are displaying "blue" (gray) colors or even black colors. Check the bellies of such fish. There is a slight difference in the belly color of most. A silver white belly indicates that there is a greater possibility of that fish retaining the black color longer. A yellowish or bronzish belly indicates that the fish will most likely change to red/orange in a bit - a month or year. Any black fish that is carrying even a spot of red has a high probability of changing to all red at some time in its life.
Black is a very difficult color to get solidly - a good black is a tough thing. What appears to be a good black for the first 4 years may bronze out or turn red or red/white after a bit.
It is rare that you will find a "black baby" fish - most will quickly revert to other colors. The older the fish is when it is still displaying full black color, the better chance you have of getting a "black fish".
I raised a set of blue Lionhead this past year. All appeared black or blue - but now that they are reaching their first birthday I would guess that over 85% of them are changing to white or white/red.

Black is tough.