When the psoas becomes tight, overworked, or shortened, it may pull the pelvis into a more forward-tilted position. This can increase the curve in the lower back and make the lower abdomen look more prominent.
This is why some people notice both:
a stiff or achy lower back
tightness in the front of the hips
difficulty standing tall after sitting
a belly that appears pushed forward
discomfort when lying flat
reduced hip mobility
The important point is that posture is only one possible explanation. A protruding lower belly is not automatically caused by the psoas. But if it appears with hip tightness and lower back stiffness, working on mobility and strength may help.