Hello,
I have experience with managing AWS cloud server.
AWS has its own control panel, which may not look exactly like a regular cpanel. But it gives you all the control.
You will first have to create a EC2 instance, a RDS database and then host the site. You may have to use Route 53 for the domain pointing. The setup also depends on your budget and how busy your website is.
I can do these setup for you. Look forward to hearing from you for further discussions.