Commands like service and systemctl mostly just don't work in Docker, and you should totally ignore them.

At the point where your entrypoint script is running, it is literally the only thing that is running. That means you don't need to restart nginx, because it hasn't started the first time yet. The standard pattern here is to use the entrypoint script to do some first-time setup; it will be passed the actual command to run as arguments, so you need to tell it to run them.

#!/bin/sh

echo "in entrypoint"
# ... do first-time setup ...

# ...then run the command, nginx or otherwise
exec "$@"

(Try running docker run --rm -it myimage /bin/sh. You will get an interactive shell in a new container, but after this first-time setup has happened.)

The one thing you do lose in your Dockerfile is the default CMD from the base image (setting an ENTRYPOINT resets that). You need to add back that CMD:

COPY entrypoint.sh /entrypoint.sh
RUN chmod +x /entrypoint.sh
ENTRYPOINT ["/entrypoint.sh"]
CMD ["nginx", "-g", "daemon off;"]

You should keep the other settings from the base image, like ENV definitions and EXPOSEd ports.