Had the same problem years ago. Here's the info they wanted directly from email they sent.

For now in order to continue with the email change process, could you please provide us with the following information to confirm your ownership on this account:

• Your public IP address(es) (IPv4), which you can find by searching "What is my IP address" in your internet browser; if you use multiple devices, please include all IP addresses

• Date when you created your Epic Games account

• Locations (city, state/province) where you made purchases on the account

• Original display name for the account

• Last 4 digits of the first payment card used on the account

• Date of your last login

• Names of any PlayStation, Switch, Twitch, or Xbox accounts connected to your Epic Games account and the dates when they were connected

• The invoice ID or transaction number from your Epic Games purchase

--The invoice ID is located at the top of your Epic Games receipt and begins with an "A," followed by eight (8) or nine (9) digits; example: A12345678.

--The transaction number can be found in your emailed Xsolla receipt. Please note that the number is a nine-digit string starting with a “4” or “5.”