Is possible to start a postgresql streaming replication using pg_dump instead of copying the database?
You cannot start streaming replication without a physical copy of the data directory; usually created with the pg_basebackup command.

The reason for this has to do with what streaming replication and WAL shipping replication do. In both cases you are applying the Write Ahead Log to the data directory using postgresql's recovery mechanism. So in order to not break database consistency you must be applying the same change set to the same starting point and you are restricted to replicating the entire database cluster. This is also why you cannot interrupt streaming or drop WAL segments, since once you have broken continuity the database server cannot guarantee that it is in a consistent state.

In postgreSQL 10 or later you could use logical replication to replicate only one database in a cluster or even a single table. And in that case you can start with a "logical copy" of the database such as are produced by pg_dump.