You can cycle with an axie in it but this is very dangerous without being able to test the water. Axies are very sensitive to ammonia and ammonia levels can spike during the cycle process. What are you using to treat the water for your tank?
Sorry, I should have been clearer in why I was asking these questions: These are all areas that can cause axolotls a great deal of stress and yours is sounding possibly stressed along with the water being cloudy.
It is normal for juvies to float for long periods of time, but as they get older, this could prove to be a sign of stress depending on how long they float and if they have difficulties going to the bottom. How big are your 2 axies?
I was concerned about the gravel because there are many posts out here where axolotls have attempted to swallow rocks the size of their heads and well, that usually doesn't end well.
I asked about the filtration because axolotls hate fast moving waters and can become very stressed. Also, some submersible filters can cause the temp of your tank to rise and that could be a problem. Can you check the temp?
Just trying to gain as much info as possible to get a good picture of what might be going on there. Thanks for your patience and hopefully we can help.