I haven’t done a product with foam before, but I believe you’ll need a mold if you want something organic. You may want to consider filling your product with Styrofoam beads instead, but it won’t be as cushy for sure.
Some distributors in China have extensive factory connections and can act as an agent between you (the designer) and the manufacturer. But to most distributors, it’s risky to develop a product themselves and then hope that someone would buy it. It’s much easier and less risky to wait for the manufacturers to solicit new products to them to sell. Plus, which factory wants to entertain with developing a product that have no guarantee of an order?
Some distributors and trading company have direct connections to retailers. If you can get a retailer to buy into your idea first, it’ll be easier for the distributor/trading company to develop the product for you because at least there is an incentive (or carrot) that’s driving everyone.