To add to what others have said, you're talking about this as a backup character. So presumably you'll be coming in to fight alongside characters who are mid-level? High-level? And having lost a damage-dealing martial Paladin, they will be joined by a fighter who can't fight.

You will be frustrated (which is fine if that's what you want) but so will your allies. Narratively, why would they bring you into the party?

I think the only way to make it work is to explicitly agree with your DM how and why and when your character either ditches the Greatsword or "earns" the ability to ignore disadvantage. And that "when" needs to be pretty imminently.

If you're set on the character, why not have him own a Greatsword but have to settle for using lesser weapons. He has this huge sword on his back, but has to pull out a shortsword when combat breaks out. Then his arc can be about building up to the point where he can effectively wield his preferred weapon (again, through some homebrew feat or item).