That stuff is implemented in Java by the Sux4J project (https://sux4j.di.unimi.it/). Happy to see this is getting into mainstream (I am the proud inventor of the name "static function" for the problem :). And yes, you can use it to build a MPHF (https://sux4j.di.unimi.it/docs/it/unimi/dsi/sux4j/mph/GOVMin...).

Note that also an MPHF, as a static function, does not store the keys. A static function assigning a different output (e.g., rank) to every key will always use more space than a MPHF because you can choose the order.