Concepts exist without words, since words are just one part of a concept, and people with left temporal brain damage can lose access to a word without losing access to the concept.

We use words to solve word-problems. Before words, people thought without words but not about word-problems. Asking for techniques for solving word-problems without words is like asking how to create potteryware without pottery. There might be some sort of isomorphism that would allow you to think about words without words, but you would mainly end up with an encipherment. That is why I asked, "Has anyone developed techniques to do math without symbol manipulation?" We use words precisely because we need to know and use their systematic properties, in a similar way that we manipulate symbols to do math.

I am not saying that we are not able to understand the meaning and referents of words without words.