You can allow anyone to host a Webex meeting with a template. You can create a template where the first person joining the meeting could host/start the meeting. Log in to uichicago.webex.com and follow the directions below:
Click on Classic View in the upper right, next to your name.
Click on Webex Meetings. (note that is says "Meeting Center" in the screenshot, this was changed in a Cisco update, but is in the same place)
Select Schedule a Meeting.
You can then check the box that says "Let anyone with a host account on this site host my meeting."
Save this as a template.
Note: After creating this template, you will be able to select this template when scheduling a meeting in Outlook.
Click Add Webex.
Click Change Settings.
Select desired template from the dropdown menu.