1. A computer-implemented method for synthesizing a block-level backup copy of a database in a storage management system based on one or more snapshots of the database, the method comprising executing on one or more computing devices the steps of: generating a first snapshot of the database, wherein the first snapshot is stored to a first storage device, wherein a database management system that executes on a client computing device component of the storage management system performs operations that change data in the database; storing, by a media agent component of the storage management system, a copy of the first snapshot to a second storage device; after the first snapshot is generated, generating a plurality of successive snapshots of the database; after each snapshot in the plurality of successive snapshots is generated, identifying, by a data agent that is associated with the database management system, a respective set of data blocks which changed in the database relative to corresponding data blocks in an immediately preceding snapshot, which set of data blocks are designated changed data blocks for the respective snapshot; extracting, by the media agent, the identified changed data blocks from the respective snapshot; storing to the second storage device, by the media agent, a plurality of incremental backups of the database corresponding to each respective snapshot in the plurality of successive snapshots, wherein the respective incremental backup comprises the extracted changed data blocks from the respective snapshot; generating, by the media agent, a synthetic full backup of the database, which represents the database at the time the most recent snapshot was generated in the plurality of successive snapshots, wherein the synthetic full backup comprises a set of pointers to the most-current data blocks in: the copy of the first snapshot and the plurality of incremental backups of the database; and storing, by the media agent to the second storage device, the synthetic full backup of the database.