You can inspect the docker image to get the bash script that's used by default and simply set a custom script without the apt-get update line

This is part of the default bash script used by the agent. You can replace that script completely, just make sure to do what the agent does there in order to start the task... Use the agent.docker_init_bash_script configuration option to specify an alternate script

Yes, thank you. That's exactly what I'm refering to.

The agent is deployed on our on-premise machines

Are you referring to a task being run by an agent running in docker mode? Where is the agent deployed?