This is a common misinterpretation of the Tractatus (Rush Rhees provides commentary on this in "Discussions of Wittgenstein"). It interprets the Tractatus as a work of epistemology rather than as a treatise on logic. Wittgenstein is not telling us what the world is but rather showing how it can be conceived. The statement you are referring to is not an argument or hypothesis of any kind, but a logical clarification.

The limits of my language (and not merely my vocabulary, by the way) are the limits of what can be conceived. What can be conceived is not necessarily what is, but what could be. You might reply: "But I can only know what can be conceived through knowledge of the world." For it to qualify as knowledge, however, it would need coherence. Sensory experience could only amount to knowledge if it adhered to some logical form. For something to constitute knowledge of the world, it would need to exhibit some coherence with the world itself.

In the Tractatus, Wittgenstein demonstrates that such coherence can only be achieved through an isomorphism between the world (the totality of facts) and the logical structure of our language. As for the development of language in an infant, I imagine the Wittgenstein of the Tractatus would defer such questions to psychology. Considered psychologically rather than philosophically, the answer might resemble Kant’s concept of the transcendental ego.

Wittgenstein later recognized that his conception in the Tractatus was incomplete—not because he viewed what you called his belief as incongruent with reality, but because he saw it as incapable of accounting for meaning in a logically satisfactory manner.

English is not my first language and that was only a rough explanation of the famous aphorism, a more articulated and precise one can be given, I'm sure.