I feel that would be extremely crowded. Adult Axolotls can grow to 13" long- 3 in a 10 gallon couldn't even stretch out without bumping each other, and maintaining water quality would be a nightmare. I like a 40 gallon breeder for 3 adults. You can probably get away with a bit smaller, but if they're going to spend their whole life in that habitat, the more room to explore the better.
Read up on cycling- it is essential to maintaining a healthy aquarium long term. Also, very little of the bacteria are living in the water column. It is much more effective to borrow a piece of used filter media to kick start your cycling bacteria than to use dirty water.
Things to keep in mind:
Cycling can take a long time- best to start 6-8 weeks before you get your Axolotl's.
Never change all your filter media at once- you will throw out your good bacteria and most likely will have to cycle again.
Clean your filter media in dirty tank water- chlorine kills your good bacteria.
Try to choose filter media that can be cleaned and reused, like sponges and ceramic media.
Buy a test kit, add ammonia daily as needed- watch for ammonia spike, then nitrite spike, when ammonia and nitrite drop to zero, you will have a nitrate reading and your tank is cycled.