There is evidence that a Jew is permitted to create a Golem (though, as @ezra points out, there is evidence the other way as well in Sanhedrin 65b). Whether or not creating one is physically possible in modern times is unclear, and it is also unclear whether the Golem of Prague actually existed.
To the extent that a Golem can be created today, is it possible for a Gentile to do so? I'm aware that the likelihood of this happening is near zero, but I'm wondering whether this is due to fundamental laws of HaShem metaphysically restricting Golem production to Jews only, or whether it is because a Gentile is practically unlikely to have sufficient motivation, education, faith, endurance, perseverance, etc. to succeed in creating a Golem.