Could zombies ever exist

The type shown in movies like "28 Days Later" or "28 Weeks Later", sure. With some qualifications, there is nothing inherently impossible in some kind of "rage" virus being created.

As to the more traditional type, that is a bit more delicate. For starters, you'll never see the comedic type that amble about saying, "Brains!" at sorority houses. Sentience either is or is not, there is no selective ability to speak one Word.

As for George Romero's Zombies, maybe, with qualifications.

It may be possible to reanimate a corpse. But what it would wish to do is speculative. It might have all the memories and intelligence as before. Or it might be a complete vegetable just lying there.

It would seem difficult for it to be in a "half way" state. Where it can move, has some memories - like of what doors are - and some rudimentary tool using ability. What would actually motivate it would be an issue, too. It would seem unlikely to care about eating.

The biggest flaw is the assumption that they would only attack humans. Zombies, like any hypothetical people infected with a "rage" virus, would attack each other, too. There is no reason to attack solely humans, and certainly no credible way to tell the difference between human and zombie, or infected and uninfected.