At least from my experience, a lot of the experiences you described have a significant environmental factor. The kid taking calc in eighth grade was tutored for years at home and therefore was able to advance in school much factor. An average US school won’t dedicate resources to advance said kid initially without the aforementioned tutoring to back up the assertion they are worth the extra resources of advanced classes (either that or a more advanced school may offer more advanced classes earlier in life). That’s not to discount said kid’s achievement - they are obviously plenty smart and hardworking, just as much as those without their opportunities, however one must consider the environmental factors.
I’ve experienced the same with Intel and (insert subject of choice) olympiads. Often times these winners have environmental support, whether it be a school program or parent who knows how to get a high schooler into a research lab and prepare a winning project, or a school that supports Olympiad studying (that’s the situation I encountered when talking to Intel winners). Again, this doesn’t discount any achiever’s hard work and talent. I also realize that these situations aren’t the case for all achievers. Some achieve without any or little outside support. This is just from my experience talking to such people (maybe its just due to the microcosm of my area).
As a student in a similar situation (average high school, taking most advanced “mainstream” courses available [i.e, no calc freshman year] but nothing crazy), the best piece of advice I can give is that the internet is your best friend. Almost all the opportunities I’ve been lucky to have had were gotten came from my own research. Apply to programs online (ex. research internships if you’re into science, selective leadership conferences if that’s more your style - I’m mostly a STEM person, so I have little experience outside of that field) even if it seems like you have no chance (don’t have the stats, don’t think you’ll ever be accepted). When your environment is stuck in mediocracy, you can only rely on yourself for opportunities. The internet, and more importantly, Google, luckily, is the perfect remedy for that. Apply to everything you can. Research everything. A 10% chance of acceptance to a program is still a 1/10 chance of being selected. And once you are selected once, once someone takes a chance on you, once luck is in your favor, you gain experience which translates into better credentials for better opportunities.
I’d like to think of myself as an example. I’m nowhere as achieved as an Intel winner or Olympiad finalist, but I’ve advanced past what anyone in my school’s immediate history has done while in high school. My school thinks I’m insane for what I do (and I’m pretty sure guidance is super annoyed that they have to send in my transcripts several times for so many programs XD), but my constant researching and applying to random things has been the most successful route to gain opportunities.
Anyway, this is just my two cents on this issue (sorry for the rant, this is just a subject I’m passionate about XD). Again, this may be due to the geographic area I’m in, but this is what I’ve garnered from life as a high school student in an average area. Also, note, said programs and opportunities are more applicable to some fields than others (ex. a bio person really needs outside resources to get into a lab while a comp sci kid can do more at home without outside help), however the general message of researching and applying and putting yourself out there is the same.
