I have a battlemaster fighter who, for flavor reasons, I would love if he could cast the spell "Suggestion". He's level 5 in fighter at the moment, and since I have a level-up in my near future, I'm looking for a path towards this spell.

It's for a low-magic community-style game, so magic items aren't likely (not to mention, may not have the same DM twice in a row!). Multiclassing is allowed (artificer is not), all my stats are above 13 except Strength (10) and Intelligence (11) thanks to Non-Variant Human!

I've already looked at taking the "Fey-Touched" feat at level 6, but as "Suggestion" is a level 2 spell, it won't do enough. Likewise, as far as I can tell, multi-classing Sorcerer or Cleric won't help me achieve this without an additional two levels.

Is there anyway I can get to the "Suggestion" spell sooner?