yes, if you're using the alfresco bundle (alfresco-community-*.bin) installer and you told it that you wanted postgresql install (you're using the bundled postgresql, not postgresql elsewhere) then there will be a postgresql directory in your alf_data directory. when you start alfresco (even if alfresco fails to start, that's fine, you just want to) check what user postgres is running as. It's likely to be running as the postgres user. If it is, then you'll need to set ownership of the postgres directory (recursively) to the postgres user. or, if not postgres, then set ownership of the alf_data/postgresql directory to whomever it's running as.
I tend not to run postgres from the bundle. Instead I use either postgres from the distribution on localhost or a database server elsewhere on the network. If you have a database server somewhere, that might be an option.