Ex-product manager of an IDE and language here. Languages, like just about anything, win because of what you can do with them: ie, value. Consider Ruby on Rails: it drove Ruby; the achievement was easily creating fullstack web apps, at just the right time. Consider VB: you could build UI apps. No languages win based on the language itself but what it lets you achieve. Usually, this is in the form of libraries:* ie, functionality that using the language lets you achieve. It's not the language, but where using the language lets you get to.
Python is a nice language, but so are others. I know of three main libraries -- three main "I can get stuff done" -- eras with Python, and I think these drove Python.
1. Beautiful Soup. Early/mid 2000s, web scraping and website / XML / HTML data manipulation were a thing; this library came along and made it easy. I'd heard of Python before on places like Slashdot; it was cool but Perl was more spoken of. Then, in my anecdotal experience, what I suddenly read about was not Perl or Python, but Beautiful Soup.
2. NumPy / SciPy. Python was apparently written with numerical computing in mind, and NumPy in its current form arrived a bit after BS. Early 2000s: stats and data vis folk were using R. By the 2010s, I was hearing about all these people that were not using R, but were using NumPy and SciPy.
3. AI. Until a few years ago, it was all SciPy, then with the current era, everyone is using Python -- for AI.
None of this is the language, per se. People were not 'using Python'; they were (say) using SciPy.
I think Python benefited hugely from having not a single "I can achieve stuff" value proposition, like VB did; it had three consecutively in a row.
These all had roots well before they became well-known. Enthusiasts, initial design, years of work and usage, and 'suddenly' out of nowhere everyone is using it. The common factor there is likely Python's design and community; there would be lower level reasons for Python's success than the things it let users achieve, and those would be, what incentivised or led to Python being used for those libraries (value enablers) in the first place. I can't speak to that; I wasn't there in the Python community in the 90s or 2000s.
[*] Not always: Rust's value is in its memory system and safety. That is not a library but inbuilt, yet that still is something you can do, a goal, value, something you achieve using the language and thus you turn to the language in order to achieve. Rust minus that would need some other reason to be used.