On its way
Short version: we do not send anything. The buy button on a card opens that piece on the shop that holds the stock, and from there the order is theirs: packing, carrier choice, tracking and the delivery window. The timings shown at that checkout, worked out for the address you type in, are the ones that apply.
Where to watch your order
The confirmation mail and the order page in the account you bought through carry the live status. We never see an individual order, so that page will always know more than we do.
If something stalls
A stalled parcel moves fastest from the order itself, through the help pages of the shop that sent it. That route can see the box; our inbox cannot.