It's hard to find non-CFI entry-level flying jobs. That's why most people get the CFI. You could network like crazy and beat the bushes for work.

Or look into banner-tow, pipeline, parachute ops, or traffic watch jobs. The downside to these is lack of IFR experience. The regionals are desperate so you'll get hired as long as you have the ATP mins, but you still have to pass training...