The 404 page is a standard response code in HTTP telling the user, in effect, that they've clicked on a broken link.
When I was Director of Ecommerce we had a period where our 404 (not found) page was shown so often it got indexed in Google. You don't want that (lol), but you DO want your 404 page to create a sense of missed opportunity.
Your "not found" page needs to create a sense of easy correction and reassurance. Your site (and by extension YOU) are for real. The 404 page that provides a sense of stability, missed opportunity and a clear path to correction can win back what might otherwise be a lost customer.
One way a website creates trust is to manage everything with a sense of commitment and quality. When our 404 page was showing up so much it got ranked I made sure to apologize and share a special offer code. There was a period when that offer was our most popular redemption (again NOT GOOD lol).
A visitor might "fish" your site typing a nonsense sequence to see what you offer. My thought was always HAVE AT IT (lol). For the honest traveler who ends up seeing your 404 (especially if YOU are at fault) having a great design and a promotion code can safe the day.