Hi. Is there any way to recover folder that was deleted by user without using catalog or machine backup?
can you check in the catalog manager?
Short answer: no
Longer answer: how should you be able to recover something deleted without using a backup? You would need the "thing" (in this case it's the OBIEE catalog) to have a kind of trash folder just like your Windows has. OBIEE catalog doesn't have that: delete means gone, bye, fully deleted.
If you don't have a backup you can start rebuilding it right now. Catalog manager is pointless without a backup for the restore.