How do I stop Avast from scanning my computer when the computer is booting?
Press Escape? 
The boot-time scan is scheduled only once - unless you schedule it again manually.
I hit escape once it starts. Is there any way to keep it from starting the scan?
As Igor said the boot-time scan is a single action operation it is scheduled by the user and operates once, so I can only assume that you aren’t talking about this, see image1 of the avast boot-time scan in operation. Is this what you are seeing ?
If not then you are seeing what an on-access resident anti-virus is all about, scanning files before they are run to stop infected files from running. Is this what you are talking about ?
If so avast is designed as a resident on-access and not an on-demand scanner, are you using another resident antivirus ?
Welcome to the forums, BigA8015.
If you have just installed avast for the first time, it will do a boot scan on the reboot. If this is a new installation, then you need to let this boot scan finish so that avast can insure that your computer is virus free in the beginning of it’s installation on your computer.
If this is not a new installation, the boot scan will only occur if you tell it to do a boot scan.