Ensure all screws are in the correct position and tightened sufficiently. Note that a screw sticking out could be causing this issue.
Next, check for any damage to the body of the phone, slightly bent? Corners caved in slightly?
Further, check that the screws in the side of the screen, holding the heat shield, are in straight and fully. Check the brackets on the side aren’t bent, if they are: when going to push the screen down, carefully use a spudger to push them inside the phone slightly
Finally, ensure the new battery is properly installed, the adhesive isn’t too thick and that it isn’t swollen already. Although rare, I have received faulty batteries that come swollen and cause this issue.
Send us a picture of where it isn’t going down, we may be able to diagnose from that.