Unfortunately, for the JetBlue card, Barclays does not give an option for a temporary number that can be issued immediately. But as OP pointed out, you can get the physical card expedited (for a fee).
i just applied for this card and was approved - I called customer service to expedite the card and they said they couldn’t. Anyone know how I can switch shipping? I have flights to book and thought I’d be able to use it immediately