Why Will Our New Masonry Fireplace Not Draw Properly?

Does the smoke only come into the room when you first light the fire?

If so, the solution is:

When all the materials are in place to light the fire, hold a bunched-up newspaper in your hand, inside the firebox, and light it on fire.  Hold it as high up as you can while you're lighting the paper/kindling of the actual fire set.

What you're doing is pre-heating the air that's in the firebox.  Warm air rises.  So by warming that before much smoke is generated, it'll draw the smoke upward immediately.

Are you sure the damper is open?  Just a little story behind this question......I was sharing an apartment with a couple of friends MANY years ago.  The apartment had a fireplace.  However we did not know that the lever that operated the opening and closing of the damper was very loose.  So, when we got the fire started and closed the wire curtain to contain sparks and such.....we accidently closed the damper and didn't know it until the smoke detectors started going off.  Just a suggestion.  Good luck....Janes