If you do sue, take eBay to court, please come back with the result, no one ever does, so it would be a learning curve for us here, to see the result of a court case.
If you have no evidence of a purchase in your eBay account, you may have made a purchase as a ' Guest Purchase' this is not a fake account, but no info will show on your eBay account.
If you have not received your item then this will explain how to claim.
https://www.ebay.co.uk/help/buying/returns-refunds/returning-item/returning-items-bought-guest?id=40...
@zur.uk.mly1amqm