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I think my first one was about the same time horizon as yours; IIRC common suggestion was 2 cycles at the latest, and if not, call.
Will also say the monitoring solutions add some time; I finally got a balance change and I was in my reports anyway for a dispute and noticed that Amex had updated right when they should've but I didn't get the alert until 4 days later.
I had the same experience with Barclay; hit my reports before the card arrived. My Amex is at 15 days, so I have a long wait ahead. Anxious for the same reason you are, the backdate.
I applied for my BCE on the 4th, received the card 6 days later and no love on my CR thus far. On the other hand, I applied for my Freedom on the same day as my BCE and Chase reported to the CB's a week ago.