Absolutely not. Your description of his theory is wrong. His argument is that humans innately possess universal grammar. That is not at all the same as “innately storing all grammar at birth.” It was obvious to him and anyone else at the time (and long before) that a kid born in America doesn’t spontaneously start speaking Swahili without first learning it. So what is universal grammar then? It’s the innate capacity for grammar itself.

Secondly, Chomsky did in fact present evidence for his theory. His most compelling evidence is summarized by the Poverty of the Stimulus argument. That is to say, human children begin to speak and understand their first language extremely rapidly given very few examples, mostly from listening to and interacting with their parents. More recently, given our experiences attempting to build AI in the form of Large Language Models, we’ve witnessed just how incredibly tiny the “training set” for human babies really is, compared to the sheer enormity of the text they feed into something like ChatGPT (a significant portion of all the text ever written in English).

This observation is what originally refuted Skinnerian behaviourist theories of language development. Skinner essentially tried to say that humans learn language by positive and negative reinforcement, the way we train a dog to do tricks. But that idea is obviously false to anyone who witnesses a child rapidly begin speaking. Language is compositional and infinitely productive, so to be able to acquire it so quickly implies that the brain is preconfigured or structured in a way that innately understands these features. That is Chomsky’s theory.