https://www.americanexperiment.org/study-finds-weak-relation...
Your $1 lottery coupon has extremely low chances of winning a million dollars, but they aren't zero. No one will sell you any stocks for $1, but even if they did what is a chance of a random $1 stock increasing in value one million times?
You have been able to buy mutual funds in dollar increments for like forever, with the significant caveat that there's often a minimum purchase amount, but once you hold that you can add in single dollars if you want +/- they only deal in a certain number of decimals.
Fractional share trading of stocks and ETFs happens at a lot of brokers for the past several years, too. Do they really want you to buy $1 of BRK.A? probably not, but you probably can.
Also, there's like penny stocks. :P
But yeah, there's no mechanism for that $1 to turn into millions of dollars within a few days. It can happen with a very well timed purchase, many decades, and some inflation, but that's not very exciting.
Just like AI p(Doom) in the next decade is approximately zero, but we all have to pretend to it's between 1 and 10% so American frontier labs can implement regulatory capture.
So if what you're saying is you are willing to bet $1 if I give you a 1 in 1 billion chance of winning $1M, I will take that bet. And I will take that bet as many times as you'd like.
But your best chance of winning $1M? Start with $10M.