As the title says. You would be pushing the 'trailer' rather than pulling it. Does this exist?
The one advantage over a trailer would be you can see your cargo.
My very basic design idea is to attach the cargo carrier to the axle of the front wheel (allowing up and down tilt to get over curbs) and have one free to castor 20" wheel in front. Steering would be harder since you have to move the whole "trailer" but it's hard to say by how much.
In summary I think it's possible to build and ride around with such a thing. But does it exist as a commercial product or diy project?
ETA: Apparently my wording was not clear enough: I'm not looking for a cargo bike with the cargo in front (like a bullit or backfiets or babboe or flying pigeon or or or ...) but for something that attaches to the bike unlike a trailer, namely in the front. Also I'm honestly at loss what to do with the answers - most of you point out relevant problems, none tackle the actual question (though the answer is likely no, and this is always hard to answer).