Hardcore is a different mode, you can’t play your softcore characters in it.
A lot of people will use Merit Tokens, available in the Forgotten Gods expansion, to skip difficulties. You can read/view how they work here, but be warned; skipping means you’re facing harder foes and will be at a disadvantage if you don’t have gear ready to use since your resistances still take the same hit/s when you skip as they do normally.
Often merits will be used to unlock the riftgates in the lower difficulties and then people leap around in those difficulties grabbing shrines for the devotion points and totems for gear before they go back to whatever difficulty they wish to play.