Unfortunately like the previous game, you can not play this game on a higher difficulty setting from the get-go, you need to complete it and then start NG+. That said, I have mainline the entire game with a trainer to give me God Mode and skipping every cutscene while trying to do very little of anything that isn't the main story so that I could play fresh with a higher difficulty setting. This is by no means perfect but it will save you from having to play through the entire game to actually be challenged. 

Some key things worth noting: 
1. I have tried my best to do as little non-story-related content as possible but some things will transfer over such as items, etc.
2. You will be under-leveled as my characters will be around level 45ish but the game recommends level 55 for Hard and level 75 for Legend. You can use Cheat Engine to help you with multiplying EXP.
3. I have barely any items, you will be significantly underpowered as you will have the uttermost basic gear. As before, you can use Cheat Engine to give yourself more money and buy top-tier gear at shops.
4. A majority of the jobs have not been levelled up. I chose what I thought was the most boring job for each character and stuck with it just so I could experience the more exciting jobs fresh. Keep in mind there was a limited selection for me as to unlock more jobs you need to progress the bonds of your party members. So expect Kiryu and the gang to be rocking a high-level lifeguard job level lol.
5. Things such as side quests, raids, mini-game progression, side activities such as Dondoko Island, etc will be reset as standard, so don't worry about missing out on any of that.
6. I caught zero Sujimon, but some are forced on you via the story missions.

All in all, this is as close to a fresh experience combined with a higher difficulty you're gonna get this early into the game's release.

A small update that some of you might find helpful. I found a really quick and easy way to level up your characters. If you can play NG+ I'm going to assume you have the Deluxe Edition and as a result, you will have 5 level boosters in your inventory. Here's what you do (people familiar with Cheat Engine will know what to do):
1. Download Cheat Engine and install it.
2. Run the game, go into your inventory, find the level-up boosters and then open Cheat Engine.
3. Click the glowing box in the top left and then choose the Infinite Wealth exe (it will have the game art icon).
4. Under Value, type in "5" and then click first scan and wait for the scan to complete.
5. Go back into the game and use one and ONLY one level booster on a character.
6. Go back to the Cheat Engine and under value type in "4" instead of 5 and click "next scan" and not first scan again.
7. Go back into the game and do this a few more times, rinse repeat but don't do it more than four times total, you need one level booster total.
8. By this point there should only be around one to three addresses found in the box to the left so double-click on all of them there.
9. Now there will be addresses on the bottom box so change the value to "5" and not more as you can only hold 5 level boosters.
10. Go back into the game and go crazy using the level booster, once you have zero go back to the Cheat Engine and under value (there should be zero now) and type in "5" again, go back to your game, leave your inventory and go right back in to refresh the supply you have back to 5/5 (it will not refresh automatically, you need to do this).