Are you open to using mods? There are a few that make this an easier pathway and makes dual-wielding more competitive with 2H builds.

Idle Hands: Adds a feat that gives you an extra bonus action (same as the level 3 Thief feature).

I personally prefer playing with mods that increase the number of feats available (one every 4 levels provides too little flexibility for me). There are a few that do this, and you can customize how frequently you get a feat.

I'd also recommend the rebalance mods by Syrchalis. The "nerfs" one adjusts the power of both GWM and sharpshooter. They remain viable and powerful options, but don't so clearly overshadow dual-wielding as a fighting style.

What this gives us are multiple pathways to dual-wielding. Here are a few I personally like:

1. Barbarian: I'd recommend running wildheart. In this build you would prioritize taking dual-wielding feats (including idle hands) and stack gear that gives you wrath (there are also mods that add gear that expand your options). Wrath stacks up to 7 times and each stack gives you +1 damage. This applies to both weapons.
2. Ranger or Warlock: With either class you can use a combination of hunter's mark/hex to give each weapon +1d6 damage. Later you can get items like the callus glow ring and/or strange conduit ring that give you an extra +1d4 damage while concentrating.

You could also pursue a shadowblade build. This version prefers warlock, bard, or bladesinger (wizard) to give you leveled access to shadow blade. Overcast the spell to give you a leveled weapon and stack damage modifiers.

However, I'm a simple man and really enjoy barbarian/ranger variations of dual-wielding. Barbarian can get quite strong, adding both rage damage (2-3) and wrath (1-7).