I am trying to recreate an Item that exists in BG3 as a Homebrew item in D&D Beyond.

When creating the item I would like the item to enable the wearer to be able to gain the Fighting Initiate Feat, however it is not listed in the feats option for homebrew items.

Is there a way to remedy this issue?

Do you have access to the content from Tasha's Cauldron of Everything? That's where Fighting Initiate is located.

I don't have access but my friend who bought it also tried, and it still was not in the list for him too.

Unfortunately, even if the feat were listed the item wouldn’t add the feat to the character sheet anyway.