first we might need a serial number from the truck dataplate to get the correct info for this truck.

my first thoughts , if there are no errors showing on the display or MIL lights lit when this occurs then there may be a stuck control sensor switch or possibly the reverse clutch pack may be hung up so when you first start the truck it causes the truck to jump briefly until it lets go and shifts back into neutral.
And yes there might be a park brake switch issue but usually if that switch is not made the truck wont start.

There are many things that could cause this symptom but as i stated, having a serial number would be more helpful to help any of us help you figure this out. (unless someone has already encountered this problem and already knows what it is). :o)