For anyone who wasn’t aware, the uterus is roughly 1"x2"x3" prior to pregnancy - on a rough par with the male prostate. Think of 3-4 large brazil nuts (in their shell, and you wouldn’t be terribly far off. (After pregnancy, its size can vary depending on many factors.)
I mention this because many people, including women (and myself, once upon a time), have a mistaken impression of how large the nongravid uterus is. The first time I held one in my hand, I knew the numbers, but I was still surprised at how tiny it was.
Because of its small size, the nongravid uterus sits much lower and deeper than most people think. Even in pregnancy, it’s not as large as people imagine until the second half. It starts plum-sized, and well below the rim of the “true” pelvis (a cup-shaped rim down in the bottom of the combined “hipbone” called “the pelvis” - the vast majority of which is anatomically known as the “false pelvis”)
At 6 weeks, it’s egg-sized; at 8 week it’s the size of a small orange; at 10 weeks, the size of a large orange. It usually can’t be felt (palpated) over the rim of the symphysis pubis (the bone in the front of your pelvis). It reaches the umbilicus (belly button) by the 20-22 weeks (just before the fetus becomes potentially viable)
Therefore, ‘the pooch’ which begins well above the pubic bone and goes up to the bellybutton is unlikely to be caused by the uterus. Many women who have never been pregnant - or for that matter, many teenagers and some preteens have ‘the pooch’.
In many women, it seems familial. In some (familial or not), it can be conditioned away by targeted exercise of the lowest abdominal muscle bands. I have no idea how one would go about cultivating one.