That is one possibility, or it could be others. An "at this time" message appears to be a new, and unfortunately somewhat non-specific Apple catch-all error message. It could mean that you cannot connect to the Apple service you need to use, or it could mean there is something else wrong in your information entry (but it doesn't tell you what exactly), and once you correct that, _then_ it is the right time. ;-)
Check if Apple's servers are working: Apple - Support - System Status
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 (e.g., missing information) you are trying to perform and once you take care of that issue then it can do it. When changing country settings Apple terms and conditions make it clear you are only supposed to do this if you are truly a proper resident in the new country and have information conforming to the new country. Their documentation is not very specific but it could be your phone number do not meet their specifications. Or it could be something else the system does not like such as a payment method from another country.
If you still have problems contact official Apple Support:
Click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.
or:
Contact Apple for support and service --> "See a list of Apple phone numbers around the world."
Click here --> Contact Apple for support and service - Apple Support