Disclosure: I represent the product I'm mentioning below
This could be done rather easily with PowerMapi, a powershell module that let's you do advance stuff with mapi directly, including outlook profiles.
I don't know the depth of the issue driving the question, but realize that this option would also require access to the module DLL on the users' hosts. If that's a blocker, disregard.
The first thing to know is that a MAPI profile can only be mostly configured, not completely. Outlook completes the configuration on first launch.
I'll assume the real request is to be able to do this change without requiring any prompting for an end user to deal with...if so, the example below will work well for that.
Furthermore, the standard way a profile is setup is very similar as you see when you create one manually from the control panel. Essentially, given a servername and mailbox identifier, a mapi method exists to "configure" the profile. This causes some communication to occur between mapi and an exchange server to fill in all the other necessary details. Then when outlook runs the next time, it logs on to the mailbox straight away and fills in any other details that Outlook needs in the profile.
$newProf = new-MapiProfile -AddExchangeMailbox -ExchangeServername ex01.contoso.com -MailboxIdentifier useralias
There are also options with the cmdlet to add an Office365 mailbox in the new profile or to setup for Outlook Anywhere connections. Look at the details for new-MapiProfile.
Be aware that the example above will still prompt for a username and password if the current user is not also the "owner" of the malibox. If the computer is not domain joined, or the user is logging in a a local user (not as a domain user), then there will be a prompt for credentials.
The new-MapiProfile cmdlet does accept credentials as a parameter, and if the creds provided have sufficient rights to access exchange, the cmdlet will complete without prompts. However, this would also mean embedding credentials into the cmdlet/script...which is generally a no-no.
Lastly, the -Credentials feature is showing not work work with Windows10 and Outlook 2013 and later because MS is changing the standard cred prompt to use the WinRT version, away from the older win32 calls. Be sure to test as always.
And finally, PowerMapi provides complete access to all properties and attributes of profiles, profile services, and profile providers. With such it is possible to pre-fill all the properties for a profile instead of having mapi do the "configure" call that requires network communication. However, that should be left for those familar with mapi.