For a fresh hero, without the campaign completed, that’s not right…
https://eu.diablo3.com/en/game/guide/gameplay/game-difficulty
When you start up a game of Diablo III, you’ll be able to select the difficulty level you’d like to play on. By default, Normal, Hard, and Expert are available. You’ll unlock Master difficulty when any of your characters completes the game, and Torment difficulty when any of your characters reaches level 60.
So, difficulty levels available to a hero are…
Level 1 - Normal, Hard, Expert
Level 1-59, with Campaign complete- Normal, Hard, Expert, Master
Level 60 - Normal, Hard, Expert, Master, Torment 1-6
Level 70 - Normal, Hard, Expert, Master, Torment 1-16
As the OP hasn’t completed the campaign, or reached level 60, the highest difficulty setting they can start a game in is Expert.
However, if they want more of a challenge it’s possible. An existing level 70 hero starts a Torment 6 game and invites them into it, then leaves the game. This leaves the sub-70 hero in a Torment 6 game (the highest difficulty a non-70 can be in) and they can level up at Torment 6, dropping down difficulty levels if they find that too difficult.