Since you haven't raise baby brine shrimp (BBS) before, start practicing (with a small amount of eggs) before you need them. They say, like, 24-36 hrs to hatch, but that is temperature dependent. Some people buy those BBS hatcheries. Regardless, that will allow you to check out your BBS hatching set-up before you need them for the baby axolotls.
Note that you will probably want to keep two alternating batches of BBS going, since your babies would get pretty hungry during the 24-36 hrs it takes for a new batch to get going.
If you have too many BBS hatching for your axolotl babies (which is far better than too few), small tropical fish love them too.
A small quantity of eggs goes a long way. Refrigerate whatever you have left to keep them viable longer.
I usually decapsulate the BBS eggs, but you probably don't want to try that until you have more experience with them. Plus, if you are only using them for baby axolotls, decapsulating them (which makes them edible without hatching) doesn't have the advantage it does with fish fry, since axolotl babies won't eat them unless they are moving like living creatures.
Don't get intimidated by BBS - they are very easy once you have an appropriate set-up.