This should be implemented on client level, not server-side. But your application can use a server-side move of course (it’s implemented).
So, your application creates a bucket called trash and moves objects to there instead of delete, then by schedule or request removes it out of there.
The same is possible to do within a bucket, using prefixes.
Perhaps the versioning could be used like this, when it would be implemented: Object Versioning · Issue #23 · storj/roadmap · GitHub