Answer

The question is not well defined. What does it mean that it is impossible to approach the Torah without faith / belief? You probably mean to ask whether commandments have value without faith / belief. In my opinion, they do not. See my article about causing a secular Jew to stumble into a transgression.
The question whether faith / belief is a commandment (this is what was asked against Maimonides, who counted faith as his first positive commandment) is unrelated to the value of commandments without faith / belief. Even if commandments had value without faith / belief, it still would not be possible to command faith / belief, because that would only mean that faith / belief has value, not that one is obligated to do it. A commandment is something one is obligated to do. Beyond that, faith / belief is a stance regarding facts, and it does not make sense to issue a command about facts.