Currently there is no known or documented way to enable a Mailbox Archive on EXO / MSO using a Restfull API. The Exchange Powershell provides a way to enable but with MFA there is no way to do that...
lindalu-MSFT
Microsoft
MicrosoftHi, we apologize for the confusion where to post your Graph feedback. This community was intended to be a temporary location to submit product feature suggestions between Microsoft moving off of UserVoice and the release of Microsoft's official Feedback portal app. Now that the latter is released, we encourage you to resubmit this great suggestion on the official Microsoft Graph Feedback portal at Microsoft Graph · Community.
Kind regards,
Linda
Microsoft 365 Developer Platform community steward