In the past, people seemed to have gotten the membership number before the welcome packet. But my recent experience was the same as yours. I received our welcome packet nearly 3 weeks ago (January 13), after our deed was recorded on December 29. I *still* have not received a membership number in the mail. I was finally able to get access to the system by calling late last week (January 28, so nearly a month after the deed was recorded). My attempt to call a few days prior to that was met with "we can't find you in the system". Others whose deeds were recorded around the same time as mine, or even shortly after, have reported success in obtaining their membership numbers over the phone much sooner, in the more typical 12-14 day range. So perhaps I was just unlucky.
I do suggest calling, unless you're in no rush to obtain access. I wanted a reservation in March, so I was getting a bit anxious.