The basic idea is: Get one extra bonus action and use Sorcerer Quickened Spell to throw out 3 (or 4 or even 5) spells/cantrips a round. It burns through spell slots very quickly but the burst damage is vicious.
Get your extra bonus action from Rogue Thief (level 3) or from Pyroquickness Hat or the Helmet of Grit. Practically, the headgear are not available until Act 3, so you want to go with Rogue.
The basic build is Rogue (Thief) 3, Sorcerer 9. Build the stats like a Sorcerer: Charisma primary. Always take Haste as a Sorcerer spell and Quickened Spell as one of the metamagics. If you want to be able to throw out AoE attacks without trashing your allies, it is Rogue (Thief) 3, Wizard 2 (Evoker), Sorcerer 7, and use the memorized Wizard spells for defenses like Shield and Absorb Elements which don't use spell DC to attack.
The build never achieves 6th level spells and the Evoker option never achieves Sorcerer 5th level spells, so your best bet is to specialize in something that can do more damage. Draconic Bloodline (Red or Gold), plus the feat Elemental Adept: Fire is a good combo.
The basic combat strategy is to use Haste (or Potion of Speed or Haste Spore Grenade) at the beginning of combat and then pump out spells (or cantrips) for every Action and Bonus Action you have every round until you burn through your spells slots. If you run out of Sorcery Points before running out of spell slots, restore them using the standard Sorcerer abilities.
There are many, many ways to get more spell slots or otherwise extend your resources:
Tactics: You can extend the working life of the spell spamming by casting cantrips with the Actions and saving the Bonus Actions for the quickened higher level spells.
Wizard: Arcane Recovery (out of combat)
Astral Tadpole: Freecast. This also saves the Sorcery Points if used on a quickened spell.
Astral Tadpole: Mind Sanctuary. No longer have to use Quicken Spells while it lasts - saves tons of Sorcery Points.
Equipment: Staff of Spellpower or Markoheshkir allow one free cast. This also saves the Sorcery Points if used on a quickened spell.
Equipment: Pearl of Power Amulet or Spell Savant Amulet allow for spell slot recovery.
Elixirs: The Elixirs of Arcane Cultivation (in any of 4 variants) give a filled spell slot. Taking the exact same one again does nothing, but you can take a different level (regular, Greater, Superior, or Supreme) and keep getting extra spell slots for as long as you have elixirs and the Bonus Action to take them.
While it would be absolutely lovely to use the Staff of Cherished Necromancy to offset some of the costs, sadly, it doesn't work out well because the best necromantic spells are 6th level and the build never gets above 5th level spells.
