It is possible.

You generally have two ways to export water to the USA:
1. You export directly to the USA, It means you will import product into the USA and resell inside the USA by yourself. This is the most complicated strategy, and if you are just starting, then I don't suggest that for you. In this case, you indeed need to have Company registered in the USA:
2. You sell to USA importer. You need to find the importer who is interested in about importing drinking water. Then you no need to register USA company, but you need to provide all needed certificates and licenses for USA importer.

Since it's only water, likely no one.

One of my companies ships fluid products from the US to Australia + shipping is a far larger expense then actual product.

Be sure your really do your market research well to determine if you can actually make a profit competing with existing US brands, after paying shipping.