At work we make websites for other companies. One of our client wanted us to make a e-commerce website for them. Nothing out of the ordinary until we realized they had 50 000+ products to sell and their classification is inexistant. In other words, we don't have ay categories to work with. They just told us to "Put a search bar and it'll be fine".

So, how would you make an e-commerce site work for the users without any kind of browsing through lists of products ? 

**EDIT**
The client is a reseller. He sells power outlets, light bulbs, electrical cords and stuff like that. The reselling part is why he doesn't have categories, because every single seller manage their own database with their own description for each product.
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Your client might not be able to assign categories to products, but there is noting stopping them assigning categories to *sellers*. 

The kind of sellers using a resale ecommerce site are likely to be specialists in certain categories already, rather than having a diverse range of products (e.g. there will likely be sellers that specialise in lightbulbs and related items). You could build loose categories around this information to augment the search functionality. For example you could have an option to "view more sellers like this", or "view all items from similar sellers".
If there is no way of categorizing the products then search must be the primary method of traversing the catalog. But as a previous answer suggests you should guide the user with top products sold for a search, top products viewed for a search etc. The other users behavior should help guide them, consider adding a method for users to tag products to build the categories may be an option. You may also be able to build a straw man structure by querying the product names for things like bulb, switch, socket etc and start with that to see what sort of a category structure may be involved.