Restore DIfferential backup on azure managed instance?
Question: Can I restore a differential backup on azure managed instance? 


No. Borrowing from my answer here, Managed Instance only supports the restore of full backups; no log or diff. See this thread:


Lesson Learned #82: Azure SQL Database Managed Instance supports only COPY_ONLY restoring a database backup


And the limited syntax diagram for RESTORE in the documentation for Managed Instance:


RESTORE Statements (Transact-SQL)


The docs imply that RESTORE ... FROM URL will implicitly add WITH RECOVERY and so there will be no opportunity for logs or diffs to be applied after the initial restore. So your downtime will be >= the time it takes to take a COPY_ONLY full backup, put it somewhere MI can access, restore it, and re-point your app(s). You might also want to read through this tutorial, for a different approach.