We have a lot of customers who host an instance of ProGet in the cloud, but we do not offer hosting at this time for a number of reasons:
better control of infrastructure; you can design your instance to fit for you, instead of in the limited buckets that would be provided
choose your own provider; instead of being forced into using whatever cloud provider (or random datacenter) we choose, you can pick the one that you use
full control over disaster recovery; no company will care about your data as much as you will, and getting a month free of hosting after losing all of your data probably isn't going to make any of your stakeholders happy
As far as how to host a ProGet instance in the cloud, you would be safe simply using built-in authentication and installing it on a public-facing server with only the HTTPS port open. "Anyone" could access the log-in page, and any feeds that you give "Anonymous" access to, but on it's own, ProGet has been pen-tested and will be secure.
You could also do any of the following:
IP Restrict at the network level
use ExpressRoute (a kind of VPN)
integrate LDAP (Azure version) instead of built-in authentication
sync Azure AD with your AD
Those are progressively more difficult to configure, so it just depends on how much effort you want in a POC.
Note: we don't recommend regular HTTP, because then a "man-in-the-middle" attack could capture authentication information. But if it's only a POC, maybe it's ok.
Finally, some articles for your consideration;
A Comparison: Artifactory vs ProGet
Azure DevOps and BuildMaster Compared - this is specific to BuildMaster, but most of the points will apply to ProGet
