You can mark or band chickens at any age. There are different ways to do it, wing bands, leg bands, toe punching. There are many different types of leg bands, some with numbers some just using color. Some plastic, some metal. A lot of us just use colored zip ties. With two separate legs to use and a few different colors you can come up with a lot of different identification systems. Green and yellow on one chicken is different from green and orange on another, for example. I use the left leg to identify year they were hatched and combinations on the right leg to identify different chickens in that year. If feather color is dramatically different I can use green and yellow on two different chickens hatched the same year if I wish. I can tell the difference in black feathers and red. You’d probably need a different color marking system since you are wanting to identify something different. Or use something different than colored leg bands or zip ties.
One of the huge problems with any leg bands is that the chicken’s legs continue to grow. If you band them before they are fully grown you need to regularly check to make sure the band is not getting too tight and endangering the chicken. I normally band mine around four months but have to cut that band off and replace it later. You just need to come up with a system that works for your unique situation.
One way to mark chicks temporarily is to use food coloring on the down. The problem with this is that they shed down and grow feathers so you often need to renew that food coloring. It’s a maintenance issue.
Different people mark eggs in incubators for different reasons. Some people put the date the egg was laid on it, maybe to help them decide which eggs have been stored how long so which do I incubate. Some people like to mark sources for whatever reasons. Some don’t mark at all. I put numbers or sometimes letters on mine using a Sharpie so I can tell which egg is in which stage of hatching. I know if an egg just pipped or if it pipped yesterday and is not progressing. Some people won’t use a Sharpie, thinking the ink will harm the chick inside, but use a pencil or something else instead. We are all unique and do things for our own reasons.