Is a Linux system without root user possible ?

To make it short, not really. But you can design your system to never have to use the root user. This is what RootAsRole aims, and the exact purpose of Linux Capabilities. Let's consider you want a system without root user and you want to setup a webserver. Firstly, let's create the apache2 user and group:

sr adduser apache2

We consider that we still use the default configuration of RootAsRole. Then, let's add a task to install apache2 with the apache2 user:

sr chsr r r_root t install_apache2 add
sr chsr r r_root t install_apache2 cmd whitelist add apt install apache2
sr chsr r r_root t install_apache2 cmd whitelist add "apt upgrade( -y)? apache2"
sr chsr r r_root t install_apache2 cred set --caps CAP_CHOWN,CAP_DAC_OVERRIDE,CAP_NET_BIND_SERVICE,CAP_SETUID --setuid apache2 --setgid apache2

Then, let's add a task to start apache2 with the apache2 user:

sr chsr r r_root t start_apache2 add
sr chsr r r_root t start_apache2 cmd whitelist add "systemctl ((re)?start|stop) apache2"
sr chsr r r_root t start_apache2 cmd whitelist add "service apache2 ((re)?start|stop)"
sr chsr r r_root t install_apache2 cred set --caps CAP_NET_BIND_SERVICE,CAP_SETUID --setuid apache2 --setgid apache2

So now you can install and start apache2 with the apache2 user:

sr apt install apache2

This should install apache2 configuration files owned by apache2 user and group. Then you can start apache2 with the apache2 user:

sr systemctl start apache2