Sometimes after making a purchase from the Origin Store, you may not receive an email containing your Product Code.
Find your code with the following:
- Restart your Origin Client. You can close your Client by clicking Origin in the menu bar and selecting Exit. Then open up the client and log-in.
- Open your My Games library and click Origin > Reload My Games
- Click on My Games
- Right-click your game’s tile and select Show Game Details.
- In the game details screen you’ll see your Product Code as well as additional information on your game.
Source: https://help.ea.com/article/how-to-find-your-origin-purchases-product-code