In a cycle you have to introduce something to produce the ammonia to start the nitrogen cycle. Some people add fish and check their levels every day to make sure they are in acceptable range for the fish. Others do fish less cycling. I have done both. Fish in takes less time but it is stressful on fish and may result in casualties. Check out this article about fish less cycling:
So my first question was basically where is the ammonia coming from? Your tap water? Have you tested straight tap water to see what the results are? And if you are planning on getting a baby axolotl you can keep it in a small container which is what I would recommend anyways. When they are so small it's hard to feed them properly. I have a baby right now. I switch it back and forth every day between two containers 100% water changes every day. You could do this while your tank is cycling and until he gets old enough.
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