It doesn't copy the Inbox structure per se, it simply creates a matching folder for any folder in the "main" mailbox to which you have applied a tag with the Archive action, and for which at least one item has expired. In other words, as items in a folder with Archive tag applied age out, they are moved to a folder with the same name within the Online archive.
The initial processing of the mailbox can take up to a week, especially considering the size in your case. Afterwards, items are moved every 2-3 days (the official SLA is one week for Exchange Online).