How can I download docker image with Dockerfile? (dind)

I use Docker in Docker concept and I would like to create an image with predownload docker images inside of that, order to speed up the testing environment startup time.
Is there any way to create a Dockerfile where I can set up which docker image should we loaded?

I try to use something similar:
RUN docker pull my/images
but it’s doesn’t work because docker daemon is not running.

Using multiple FROM is not suitable for me.