Most of my research was toward the endurance style but I'd be sure the more road/race styles are priced similarly.
You can get an Aluminum frame/105 groupset/disc bike for well under $2K from pretty much all the major manufacturers.
for example:
https://www.cannondale.com/en/USA/Bi...9-dc76fca46582
To stay under $2K and get a carbon frame, you will need to drop to a lesser groupset or look for closeouts. Giant and Trek always seem to have some good sales.
Edit: Or go with Canyon, LOL.