A comparison with a roughly equivalent company gives some idea...

A comparison with a roughly equivalent company gives some idea of what it might be worth. Next Investors make a comparison between Argosy Minerals (lithium projects in Argentina and Nevada).
They note AGY has a resource of ~732kt of lithium carbonate equivalent and a market cap of around $48m (although it is a bit more advanced on the road to production than PUR. PUR has a bigger and higher quality resource at around 1.1Mt of lithium carbonate equivalent and has a market cap of around $10m.
On that basis I reckon a market cap at least double what it is now is a reasonable guess.
The * interview with CEO Aaron Revelle gives reason to thing a significant re-rate is on the near term cards. In that interview he says that following the spectacular recent drill results, PUR's attention is now on bringing their 250tpa pilot plant on line, with the their first run of lithium carbonate production over the course of the next couple of weeks. He notes that PUR will be looking to send product samples to potential offtake partners.
Looks like exciting news and a tick up is in the imminent offing.

That video interview is available on https://**promotion blocked**/*-tv/long-shortz/long-shortz-with-pursuit-minerals-its-more-than-a-million-tonnes-now-at-rio-grande-sur/