Looks like the way MyBinder launches render the preview using nbviewer would be a good guide good for this. This below is the pertinent code from the source of the page you get if you go to https://github.com/binder-examples/conda and hit ‘launch binder’ and then scroll down on the page:
You’ll see that URL (https://nbviewer.jupyter.org/github/binder-examples/conda_environment/blob/HEAD/index.ipynb) just points nbviewer’s renderer at the GitHub source for the notebook json code. The nbviewer render experience is more full-featured in several ways than the one in use by GitHub, even though GitHub’s support has continued to improve even as recent as last November.
That corresponding iframe will show up on the launch page right below the text that says “Here’s a non-interactive preview on nbviewer while we start a server for you. Your binder will open automatically when it is ready.” The top part of that iframe is featured in the bottom of the following image.