If we didn’t have immunity it would be unlike any other respiratory virus known to man. All other corona viruses have non-insignificant periods of immunity.

Further Fauci himself says it’s very likely there is immunity: https://www.google.com/amp/s/www.newsweek.com/fauci-really-c...

There was also a study performed on monkeys showing immunity: https://www.biorxiv.org/content/10.1101/2020.03.13.990226v1