What are the chances of attending Harvard / Stanford later in life? I have a life goal of going there but the older I get (24 now), the less I believe it can form into a reality.
But why those two? Even if you are solely focused on prestige in the most superficial sense, there are at least a few more comparable US universities. You could increase your number of options by 5x or 10x even being very picky.
These classes are offered under a program called "Harvard Extension School", and they are the same exact classes that students who got accepted the "normal" way, take.
It even gets you a degree.
If what you care about is the education and resources offered by Harvard, they are available for the taking, and they are the same exact classes offered to "regular" students.
My last class, in the fall, was a course that was offered online for the first time ever. We had a bunch of Harvard College students in-person and a bunch of Harvard Extension students online watching the lectures live (they are also recorded). Office hours with TAs were live-streamed and interactive between in-person and online students, we had the same homework and exams, etc. The professor even gave out his cell phone number so we could text questions directly to him.
The professor asked us all about our interest in a particular class that they had been asked about offering online. As it turns out, Harvard is fairly open about offering almost any of their courses online if you can show that demand warrants it, the professor supports it, and that you can get the TA slots filled.
The only downside is very very few show up for class since they're often taped and can be viewed remotely, which makes for a strange dynamic. Teachers watch the class for feedback, and its difficult to teach against nothing. My genomics class had about 5-6 people actually going to the class, but about 30-40 showing up for the exams.
(my credentials: I graded for Harvard Extension School multivar calc one summer. That guy was far from a harvard professor....)