Check what you are doing is valid and has all the information required. Sometimes an "at this time" message doesn't really mean something isn't working now but might be later; it instead can mean there is some other issue with the validity of the action you are trying to perform and once you take care of that issue then it can do it. Check Apple's documentation about the action you are trying to do.
This document explains how to create a new Apple ID (create an Apple Account) --> How to create a new Apple ID - Apple Support
Here's how you change the email address (Apple ID) you use for your Apple Account while retaining everything in your account:
1. Go to https://appleid.apple.com and sign in.
2. In the Sign-In and Security section, choose Apple ID.
3. Enter the email address that you want to use as your Apple ID.
4. Choose Change Apple ID.
5. If you changed your Apple ID to a third-party email address, check your old ID email for a verification code, then enter the code. Learn what to do if you didn't get the email. --> If you didn't receive your verification or reset email - Apple Support
6. If you use services like iCloud or Messages to share with friends and colleagues, sign in to those services with your updated Apple ID. --> What to do after you change your Apple ID or password - Apple Support
For more details, read the document: "Change your Apple ID" --> Change your Apple ID - Apple Support
From:
Change your Apple ID - Apple Support
- There's special instructions if you want to change your Apple ID to an @icloud.com address.
"If you try to change your Apple ID to an @icloud.com email address that was created within the last 30 days, you will be asked to try again later."