I can only find info about gradual long-term deficiency where a person consumes sodium but too little, and about conditions, treatments, or extreme perspiration/exercise that can cause serious sodium deficiency.
But how long can a healthy adult not engaged in strenuous activity go without consuming sodium before serious problems manifest.
There are a lot of factors but definitely not long. You’ll feel sick pretty fast, likely within a day or two. Water washes out our electrolytes and we need salt to absorb water into our cells. Have you heard about that person who died from a water drinking contest? They drank so much water in short time that their electrolytes became depleted and they died, likely from cardiac arrest. It would just happen more slowly with normal water intake without salt. I doubt this has been tested, though, as it would be pretty inhumane.