@234139623 I've split your comment into its own thread because the other one was a bit old.
Can you list what kind of proof you've provided to CS that was deemed insufficient? And which pack(s) are affected? Also, please confirm that you're trying to use a Steam key.
Is it possible that you registered the key(s) at some point previously? Even if you never used Origin, it and the Sims 3 store share information. In this case, you'd need to ask that this account be merged with your current one, and then your pack(s) would be added to your Origin library.
If you never used the code, it might be best to contact Steam instead. You can provide its CS rep with the reply from EA and ask that you be issued a new key. I'm not sure how Steam customer support works, but because it's an authorized third-party seller of TS3, it's responsible for ensuring that it delivers the product, which in this case includes a working code.
Are you entering them in the correct section? I know I made a mistake when I had bought some DLC's on Steam. I tried entering the codes in "Redeem A Code", but for the keys you get from Steam for the game and the DLC's you need to enter the codes in "Register A Game".