Arriving at a generally accepted scientific definition of AGI might be difficult, but a more achievable goal might be to arrive at a scientific way to determine something is
not AGI. And while I'm not an expert in the field, I would certainly think a strong contender for relevant criteria would be an inability to process information in a way other than the one a system was explicitly programmed to, even if the new way of processing information was very related to the pre-existing method. Most humans playing Wordle for the first time probably weren't used to thinking about words that way either, but they were able to adapt because they actually understand how letters and words work.
I'm sure one could train an LLM to be awesome at Wordle, but from an AGI perspective the fact that you'd have to do so proves it's not a path to AGI. The Wordle dominating LLM would presumably be perplexed by the next clever word game until trained on thinking about information that way, while a human doesn't need to absorb billions of examples to figure it out.
I was originally pretty bullish on LLMs, but now I'm equally convinced that while they probably have some interesting applications, they're a dead-end from a legitimate AGI perspective.