Yes, "they" can, just nowhere nearly as economically as diamonds. Synthetic diamonds go back to the 1960's. It's only lately that it's become economical.
I do doubt that gold will be economically synthesized any time soon.
Gold can't be synthesized in any practical way. Gold is an element and unlike diamonds which are just an allotropic form of carbon, gold is not a form of something else. In fact gold isn't even on the normal chain of events in nuclear fusion and is only created in nature by supernovas. However it can be created in a nuclear reactor by bombarding either platinum (more expensive than gold to start with) or mercury but alas only radioactive gold is created and then it decays into something else.