Supernovae, originally. As the Earth cooled, salts in rocks dissolved. When the Arctic Ocean started mixing with other oceans, the brine was entrained in over time.
I left out lots of stuff, like chemical weathering, thermohaline circulation, glacial damming, and Milankovich cycles which probably explain a lot more... but I’m a climatologist not a geologist so there’s a whole lot more about the chemistry I don’t understand.
And pedagogy.
Hazen's mineral evolution story was made into a NOVA. Some years back, before the NOVA, it had anecdotally been used down to high-school, but he didn't know of any attempts at middle or primary school. But it seems the usual science education dynamic is no one trying, or doing a miserable job of it, rather than hitting a rigid accessibility envelope.
The cluefulness cost space can be surprisingly shaped. Teach a 5-year old that sunlight is white, and so is the Sun, and after that second bit, they're already less confused there than most first-tier astronomy and physical sciences graduate students. I suggest we've little idea yet how early much of science might be taught, because we've been half-assing it.
This might be misread as a primordial origin event. Ocean chlorine and sodium residence times are under 100 Myr. So an ongoing process, with rocks dissolving, and excess precipitating.
When had most of the salt dissolved into the sea?