Within 24 or 48 hours of your payment, depending on which the store chose. Those are the only two options, and 48 hours is the most any store can take.
When the clock starts
When you pay. Not when the seller wakes up, and not when the show ends.
So a win paid at 11pm on a Saturday under a 24-hour deadline is due by 11pm on Sunday. That is worth knowing in both directions: it is why orders often go out faster than you expect, and why a Sunday evening payment can sit until Monday if the store is closed that day.
The seller's closed days count
A store sets its own working days and holidays, and a dispatch deadline never lands on a day the store is shut. A seller closed on Sundays who takes an order on Saturday night is not late on Monday.
This is why the estimate you were shown at checkout is better information than the arithmetic you can do yourself.
Where to see the deadline
The order, and the listing's delivery information. A courier order shows what it is due by, and once it has gone you get the tracking.
What "sent" actually means
The seller handed the parcel over or the courier collected it, and they marked it shipped. Marking is not optional busywork — it is measured, and an order posted on time but marked two days late counts as late.
So if an order says shipped, it has physically gone.
Made-to-order is different
An item being made for you runs on Days to make it instead, which is usually much longer and is stated on the listing. A cake or a commissioned piece is not a 24-hour dispatch and was never offered as one.
If the store caps how much it takes in a day, you may also have been shown a queue position before you paid — when it starts, when it is ready, when it reaches you. How a store caps its day.
Pickup is not dispatch
A collection order is ready rather than sent, and you have a collect-by window — 72 hours by default, though the store can set its own. How pickup works.
If the deadline has passed
Message the seller first. Most late dispatches are a courier that did not turn up or a parcel that went out unmarked, and both are answered in one reply.
If there is no answer and no movement, raise it from the order. Late shipping is one of six things Metzee measures a store on, so it is not a complaint that goes nowhere.
More: how to track an order, my order has no tracking number, how delivery is charged.