Sharepoint - Site Creation / Provisioning in SharePoint Online (using site templates)

Sure, you can run powershell scripts, it's just a different set of objects that are available. There are SharePoint online cmdlets available, though they are pretty limited in capabilities. But you can also write CSOM code in PowerShell. Just search for "sharepoint csom powershell", and you'll turn up lots of examples. But you should also know about the PnP project on github. That project includes dozens of powershell commands that other folks have written that work with SharePoint online, including commands to create new sites, webs, lists, etc.

You can use SPD workflows to provision the site which we have implemented for the Microsoft SharePoint online site.

In SP 2013 workflow there is a new action "Call HTTP web service" which takes the REST API calls.

With assumption that it is about Site Collection creation, (as web can be created by power users themselves) you may also create an .net executable using CSOM which can fetch details from the list and create site collections using CSOM. Executable will need to be scheduled on azure or local server.

If you need to create Web also, that can also be done using same method.

Check Create Site Collection using CSOM