chmod 666

Yup, it can be edited. This is not Reddit. :)

Done. Thanks!

@Ging @nutbutter it's freedom of init system choice!

And then apt?

Oh that's nasty. Yeah, do it!

This should work. Add a file /home/username/.config/systemd/user/my_cool_service.service with this content:

[Unit]
Description=My cool service

[Service]
Type=oneshot
ExecStart=/home/username/my_cool_script.sh

[Install]
WantedBy=default.target

Now add the script /home/username/my_cool_script.sh.

#!/bin/bash
echo "Hello from my cool script."

Enable and run the service.

$ chmod +x /home/username/my_cool_script.sh
$ systemctl --user daemon-reload
$ systemctl --user enable my_cool_service.service
# Optional:
$ systemctl --user start my_cool_service.service 
$ journalctl -e --user-unit=my_cool_service # You should see the echoed string from the script.

The service should now run every time the user username logs in.

Did you set the WantedBy field?

Did you systemctl enable the service?