Sounds tricky, not sure you can do anything clever with the Oracle redo log files you’d have to check with support, but I doubt it.
You could always got for a logical replication type move, using snapshots, but it depends on your data volumes. All systems have quiter periods and you could use that time to do the cut over.
If your DB is small enough and you do have some downtime then you may be able to migrate.
There will be a time when you’ll need to do a cut over where you app servers/clients all point to the new instance.
So how big is the DB, and how 24/7?