The Son also conveys a desire to Anakin about ruling the Galaxy, which ends up being the sales pitch that gets Anakin to join him, meaning he has a sense (albeit a twisted one) about what it takes to rule. The Son also has a lot of experience being exposed to the idea of Balance in the Force from The Father, which could explain why Snoke chooses Ben Solo, who supposedly holds both sides of the Force in him, as his apprentice and Leader of The Knights of Ren.
Not only that, it is described that Snoke develops a fascination for the Skywalker family, which would make sense especially if he’s met one before.