Stone Sorcerer makes it possible without the paladin levels. You get a +1 boost to HP every level, making you equivalent to a d8 for max HP. You get Con-based AC and Con save proficiency, eliminating some of the MAD you'd experience normally trying to make a sorcerer that has sufficient HP, AC, and Con to maintain concentration on the front line. Take Shield as a 1st level spell and don't be afraid to use it. Take Blur when you get level 2 spells and abuse quicken to get your protective buffs up and still make attacks.
You can take a spell list that minimizes the necessity of Charisma if you want to focus on weapons. Take Booming Blade and Green-Flame Blade in your starting cantrip suite. Use something like Sleep for control at low levels and retrain it later. Haste, Fly, Greater Invisibility, Animate Objects, etc. will make you better at attacking things without using your Charisma. That should allow you to buy a decent Strength score at the start to use the martial weapon proficiency granted by the archetype.
I'm currently playing a sorcerer like this that has survived with no close calls up to level 6 so far. My experience is colored a bit by using a DM-granted array with a free feat at creation, so I was able to play a Scourge Aasimar.
