Run SQL Server Snapshot Agent automatically
I believe you are looking for sp_startpublication_snapshot.  You'll want to execute this at the Publisher on the publication database.

Regarding the error: from a path could not be read, you'll want to ensure the Snapshot Agent process account has sufficient permissions to generate the snapshot.  The process account needs the following permissions per BOL:


At minimum, be a member of the db_owner fixed database role in the distribution database.
Have write permissions on the snapshot share.
The account that is used to connect to the Publisher must at minimum
be a member of the db_owner fixed database role in the publication
database.


This is covered in Replication Agent Security Model.