Salt is commonly mined where there is no local source of salty seawater. Rock salt forms as the buried remains of dried up seabeds and inland saltwater lakes. There are layers of salt hundreds of meters thick in some places, such as under the Mediterranean.
Underground Salt Mines
One estimate I saw was that the mines under the med could provide all of humanities salt needs for the next one hundred million years. From that source alone.
As for your supposition that primitive people would have had ways to extract salt from their environment in the absence of salt water, I think this is highly unlikely. Salt was historically highly prized, both for it's preservative value for storing food but also for flavour and (not understood at the time) necessary trace minerals. It almost certainly would have been traded extensively and over long distances, but unlike other trade goods like stone tools, jewellery, shells etc... it would have left no trace on the archaeological record.
For evidence that it was historically highly valued; roman soldiers were often paid in salt. Thus your "salary" was literally the salt you were paid for working. Elsewhere there are evaporation ponds along coast lines that date back thousands of years, where salt was extracted from seawater in hot climates using the sun. I also once visited a site in Scotland which had evidence of an illegal historical salt production site. Salt was taxed and regulated so on remote islands, where coal deposits were near the coast, there was a thriving blackmarket production in salt. I'm not sure of the exact age of the one I saw on Arran, but it was a few hundred years old at least.
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