But how would you compete against the established companies? It cannot be higher returns, because all index-funds are supposed to have roughly the same returns (if they mirror the same index).

So it must be lower fees. And you are able to charge lower fees if the total amount of money you manage is big. (Because a tiny percentage of a huge sum will still cover your costs.) The established players already manage a few trillion dollars, so it is hard to compete against them in this area.