A couple of things to mention here.
First, the Vagrant box is intended only for local testing and development - it is NOT intended for use in a production environment! If you want your AtoM site to be persistent and available on the web for others to use, we strongly recommend a full server installation as outlined in our documentation, here:
You can certainly create a production-ready installation using virtualization, but the Vagrant box has limited resources assigned to it and is intended for use on a local computer.
Second, setting up HTTPS is a webserver configuration issue, to be handled separately from AtoM installation. It's not something we maintain documentation for. Generally, it involves getting a certificate from a Certificate Authority (CA) for your domain. However, Artefactual makes use of LetsEncrypt
for our hosting services, which is a free, automated CA. I've never tried to set up a certificate for a local Vagrant box since they are not generally available on the web, but you could look into it with them: