Alien registration number (A#) is for registration as a permanent resident (green card holder). Green card old name is called "Alien Registration Card", new name: permanent resident card. So, theoretically you only can get the A# when you become a green card holder though normally the A# in your I-485 receipt is used as the A# of green card. But sometimes may be different.
Here are some examples similar to your case (you can find more such cases by google):