Install from source - Step missing for Arch Linux
After installing PostgreSQL on Arch (and maybe other distros too), an extra step is required to initialize the database cluster. If using the default location (/var/lib/postgres/data), this must be done as the user "postgres" who owns the folder (access rights are 700).
sudo -iu postgres
Then as "postgres"
initdb -D /var/lib/postgres/data
Source : ArchWiki