I’m curious what others have to say on the matter, but I’d say it’s never too early to start listening! And in fact, many learners (myself included!) listen way too little, especially in the beginning. Mass input is the prerequisite to output; you can’t know what word to say/write until you’ve heard/read of it at least once (unless you’re a heritage speaker and can just word-build grammatically correct-ish neologisms on the fly). For some other languages I’ve studied, I’ve purposefully ignored the written language and only focused on mass listening comprehension and speaking in the beginning.
The trick, just like with reading though, is finding the sweet spot with comprehensible input. If you pick something too far above your level with lots of words you don’t know and haven’t already encountered in some form, you won’t just magically understand it by listening to it on repeat (unless you already know lots of the words and can pick it up the few unknowns by their surrounding context). So something like an audio recording of a graded reader that you know all the words to when you read is great material to listen to.
I don’t have any studies to cite off hand, but as far as measurably improving listening comprehension, almost everything I’ve read about passive listening is that it’s basically a complete waste of time compared to active, focused listening. Having said that, I think there’s some value at the very beginner stage for more passive listening. It can give a learner an overall feel for the prosody and rhythm of a language and help them just get comfortable with listening to it in general.
Following a standard is important because as a foreigner, you will have an accent. (Almost) everyone in China is exposed to putonghua (or guoyu in Taiwan) and will be used to it as a reference point since it is taught in school and used in media. If you can mimic it well, you will be understood in most places you go by most people; the same can’t be said for a more regional accent. You can always add in a more specific local accent further down the road.
But for listening comprehension, something like textbook putonghua or guoyu is a good starting point. Some TV shows and media, even Chinese youtubers will follow the standard pronunciations more or less, and there’s no one other regional accent that’s more standardized or widespread; investing in it is the best bang for your buck as a learner as far as depth and breadth of media available. And ultimately, no one textbook or series of audio recordings will ever properly prepare you for the true variation that is listening to real life native speakers. Mass exposure is the way, possibly the only way.
So get listening, enjoy the challenge, and celebrate all the small victories and improvements along the way!