If you are the admin of a Fabric node, in theory you could write a client application that connects to LevelDB to query data. But you would have to understand Fabric data storage internals, and stop the peer process while connecting, so it isn’t really a feasible approach for users.

Another option is taking a snapshot of a peer’s channel. This will output the state database content for the purpose of joining another peer from the current state snapshot, and for comparing snapshots across peers to verify ledger integrity. Again, the snapshot is in an internal format optimized for Fabric utilities, but you could in theory write a utility to parse it with some Fabric internals knowledge (not quite as difficult as writing a LevelDB application). If you do write a utility, please contribute it back!

See the ledger snapshot doc - https://hyperledger-fabric.readthedocs.io/en/latest/peer_ledger_snapshot.html