Hard mode will most likely be "do the story". If we want to follow the trend of previous Extreme Primals, Extreme will require that Hard be beaten of course as well as the defeat of either Leviathan and/or King Mog Extreme.

There's no confirmation, but it would be odd if Ramuh Extreme has no gate from the outset. It could be argued that Levi/Mog are "unrelated" to Ramuh, but it can also be argued that Garuda/Titan/Ifrit are unrelated to Levi and Mog and they were a gate anyway. I'd say expect one and then you can be pleasantly surprised if there isn't.