If you order something from eBay and the eBay seller does not ship the item then you can file a claim with Paypal and eBay for an item not received claim.
However you must wait until after the estimated delivery time to file a claim and must wait usually a few days after the estimated delivery time.
Sellers can set their own handling time on eBay purchases but most eBay sellers will process the orders and ship them within a few days of ordering them.
Also not every seller on eBay buys tracking information or provides tracking information so the item may be shipped but you may not know about it.
You can ask the eBay seller if they have a tracking number and sometimes they will have one and provide it to you.
But if the eBay seller really did not ship the item to you and you paid for the item then you can do a charge back on your credit card or debit card or do a dispute with Paypal or eBay.
An eBay seller should ship the items you purchased or the item you purchased within 1 to 4 days of purchasing it.
Some eBay sellers that just sell part time or are just selling a few things will usually have jobs outside of eBay which means they are not watching their eBay account at all times.
So you may order something or win an auction from someone on eBay and the seller may be gone away at their other job.
So they won't be able to get to the order until after work.
So as long as the small eBay seller ships within 4 days then I would not worry.
If the eBay seller is a large company selling on eBay or has a physical office and shipping department then the seller should process the order the same day or within 2 days of ordering it and then ship it out.
On most eBay orders where I've ordered from a business the orders got processed the same day and shipped the same day.
However for smaller eBay sellers they may not be able to do that and sometimes I've had it take 2 to 4 days for a small part time eBay seller to process the order and ship.
I'm okay with that as I understand they are busy with other things.
Not all eBay sellers always mark as shipped on the items they sell or the items you purchase.
The eBay seller if they are a small eBay seller may not mark the item as shipped even though they have shipped it and not all small eBay sellers will use tracking information either.
If the eBay seller uses online postage and buys the postage with online tracking the information will get uploaded to eBay automatically and the item will be marked as shipped and a tracking number provided.
But some eBay sellers who sell a few items here and their may just go to the post office with your package and pay for the postage without any tracking number.
Then the seller may or may not mark the item as shipped or give you a tracking number even if they do have one.
If the package does not arrive on time or after the estimated arrival time then you can contact the seller and if no response within a few days you can report it to eBay.
Also some small eBay sellers only sell part time and have jobs outside of eBay so even if you order something or win an auction on something on eBay the seller may not be able to get to their eBay account and check the orders and ship them out until after work.
If it's on a weekend or during a time when the post office is closed the seller may still process your order after they get home from work and then print the shipping label or at least have it packed and ready to go the next day if it's a day when the post office is open or when UPS or other shippers pick up.