If you take abstraction to the extreme, sure - our brain is the same as GPT-3; but only in the same sense in which our brain is equivalent to any function with discrete output - that is, our brain maps something (the space of all sensory inputs) to something else (the space of mental states). In this same sense, our brain is just like the whole universe, which is just a function from the entire world at time t to the world at time t+x.
If we look at anything more specific than 'mathematical function', our brain is nothing like GPT-3. GPT-3 is not trained on sensory data about the world, it is trained on letters of text which have nothing directly to do with the world. The brain has plenty of structure and knowledge that is not learned (except in a very roundabout way, through evolution)*. GPT-3 is lacking any sort of survivalist motivation, which the brain obviously has. The implementation substrate is obviously not even slightly similar. The brain has numerous specialized functions, most of which have nothing to do with language, while GPT-3 has a single kind of functionality and is entirely concerned with language.
And even if I start writing down random words, what I'm doing is not in any way similar to GPT-3, and my output won't be either. It will probably be quasi-random non-language (words strung together without grammar) vaguely related to various desires of my subconscious. What it will NOT be is definitely not a plausible sounding block of text that I determine to resemble as closely as possible some sequence of tokens that I observed before, which is what GPT-3 outputs.
I do not have an inner GPT-3. The way I use language is by converting some inner thought structure that i have decided to communicate into a langauge I know, via some 1:1 mapping of internal concepts to language structures (words, phrases). In particular, even the basics here are different: letters, the things GPT-3 is trained on, are completely irrelevant to human language use outside of writing. People express themselves in words and phrases, and learn language at that level. Decomposing words into sounds/letters is an artificial, approximate model that we have chosen to use for various reasons, but it is not intrinsic to language, and it doesn't come naturally to any language users (you have to learn the canonical spelling for any word, and even the canonical pronunciation; and there is significant semantic info not captured directly in the letters/sounds of one word, through inflection, or tonality and accent; or in sign languages, there is often no decomposition of words equivalent to letters).
* if you don't believe that the brain comes with much knowledge built-in, you'll have to explain how most mammals learn by example how to walk, run, and jump within minutes to hours of birth - what is the data set they are using to learn these extremely complex motor skills, including the perception skills necessary to do so.