You may grant yourself the necessary permissions assuming you have the right to edit PostgreSQL configuration under /etc/postgresql.
First, check what version of PostgreSQL is installed and the name of the cluster/instance (see the output of pg_lsclusters). For instance with Ubuntu 16.04 the version would be 9.5 with the default repository because that's what was current in 2016, and the instance would be named main.
In this case, the configuration is under /etc/postgresql/9.5/main (otherwise change the path according to version/cluster). In the configuration, you may declare a mapping from your Unix user name to the postgres superuser database account, for instance:
In /etc/postgresql/9.5/main/pg_ident.conf
# MAPNAME SYSTEM-USERNAME PG-USERNAME
mymap myusername postgres
In /etc/postgresql/9.5/main/pg_hba.conf, as the first rule (the order does matter):
# local DATABASE USER METHOD [OPTIONS]
local all postgres peer map=mymap
Then reload (sudo pg_ctlcluster 9.5 main reload), and the Unix myusername account should be able to connect locally as superuser with:
$ psql -U postgres -d postgres
Otherwise check the server logs under /var/log/postgresql