Introduction

Here's how to quickly level a new character through the early game if you have some required items. It does require you to already have a character in Ultimate with revered status with the Malmouth Resistance Faction.

Prerequisite

There are two required items for this strategy:

Savior's Merits - can be purchased by a character after finishing Act 1 and talking to The Emissary to go to the Conclave of the Three on Elite or Ultimate respectively.
Potion of Clarity - can be purchased from the Malmouth Resistance faction vendor on reaching _Revered_ faction status, for the price of 40,000 Iron Bits.

Steps

Normal

Get 5 devotion points in the Crucible.
Access Normal difficulty and use the Savior's Merit and Potion of Clarity. Grab some Aether Crystals, Scraps, and Dynamites from your shared stash if you have them.
Head to the Burial Cave to kill Kyzogg the Reanimator and restore the devotion shrine near him.
Teleport to the Warden's Lab rift and move backward to restore the devotion shrine in the Underground Transit.
Teleport to the Arkovian Foothills rift. Move northwest to find the elder and take his relic, clear the blockade with your dynamite and then restore the devotion shrine on the trail past the blockade.
Teleport to the Wightmire rift and go into the cave in the Slith area for the devotion shrine.
Head back to the Rover camp to turn in the quests, keep the relic and head south to a cave and restore the devotion shrine inside.
Head to Devil's Crossing and hand in all the quests.

Elite - 1st run

Now switch to Elite difficulty and use the Potion of Clarity again.
Head to the Burial Cave to kill Kyzogg the Reanimator and restore the devotion shrine near him.
Head to Devil's Crossing to hand in the quest again. then, Give your Aether Crystals to Kasparov and Scraps to Barnabas. Also, Talk to Sahdia for some easy EXP.

Ultimate

Head to Ultimate and use the Potion of Clarity again.
Follow the same steps as the start of Elite difficulty. Kill the reanimator, restore the devotion shrine, turn in the quest, give Aether Crystals to Kasparov, and Scraps to Barnabas. Talk to Sahdia.

Elite - 2nd run

Now head back to Elite difficulty and take Potion of Clarity before doing some quests.
Kill Viloth the Corruptor in Devil's Aquifer.
Teleport to the Foggy Bank rift and move backward to kill Milton Heart.
Teleport to the Lower Crossing rift and kill Farros the Rotted .Then access the Wightmire rift and kill Jillius the Decayed and Neegan, The Withered.
Teleport to the Burrwitch Outskirts rift and complete the Tale of Two Blacksmiths quest.
Teleport to the Burrwitch Village rift and secure it for the quest.
Head south along the road and kill Balros and Hagra.
Teleport to the Warden’s Cellar rift and progress backward to restore the devotion shrine.Then head down to the dank cellar and save Kasparov's apprentice.
Turn in all the quests at Devil's Crossing.
Teleport to the Warden’s Lab rift and move north and kill the warden.
Repair the bridge in Devil's Crossing cross to the other side and proceed with the rest of the quests in Elite.