You seem to know very little about sex differences in human anatomy and physiology; the markedly different ways humans physically develop and change over the course of our lives; and the dramatically different life experiences of males and females because of our different anatomy and physiology - and the fact that girls and women go through, or are at risk of going through, many additional bodily processes that males don't experience.
In fact, scientists have documented hundreds of physical differences between the sexes of myriad different kinds which involve most of the body's many different organs, tissues, fluids, cells, genes and processes. For example, starting at birth there are marked differences in the airway cells, secretions and overall respiratory function in males and females - and also in the ways that the two sexes breathe, and the amount of energy and exertion it takes for males and females to move the same amount of air in and out of the lungs. This is one of the reasons why cystic fibrosis has a different trajectory in males and females even when they are siblings in the same family and their CF is caused by the same gene mutation(s).
At 6 months of age, the left ventricles of baby boys' hearts are on average 6-8% larger and more powerful than the LVs of baby girls of their peers who are of similar length and weight. Since the LV is the pump that sends oxygenated blood to the rest of the body, this gives male babies and children a huge leg up over female children in all sorts of physical tasks.
In the era of cell biology and genetics, scientists have found that the differences between the ways male and female cells function and the way the genes work in the two sexes, the physical differences between males and females work number in the thousands. Already more than 6,500 differences have been found in the way the same genes are expressed in the two sexes.
You also seem totally unaware that one of the reasons males are advantaged in sports has nothing to do with testosterone - it's simply because males go through none of the sex-specific processes that female humans go through as a matter of course which greatly affect our sports fitness, training and performance. Such as the 28 day ovulation-menstruation cycle; periods; menstrual cramps; heavy blood loss and clotting; PMDD/PMS; pregnancy; labor; childbirth; childbirth injuries; miscarriage; abortion; stillbirth; lactation; weaning; peri menopause; full menopause; and the host of gynecological problems like ovarian cysts, fibroids, endometriosis and chronic pelvic pain that affect so many girls and women.
Not all the physical differences between the two sexes translate into an advantage for males in terms of sports. Moreover, many of the differences give females an advantage entirely apart from sports. For example, girl babies are more likely than male babies to survive past the first year even when boys are fed and cared for more; women have better immune function; and women live longer than men.
But back to the specific context of sports: your contention that the male physical advantage in sports "is just our belief, not objectively verifiable fact" is nonsense. And it's just plain nuts - which I guess is to be expected from someone who goes by the handle "testy."
Someone from WA told the press a couple of years ago that there's plenty of documents going back more than 100 years that provide indisputable proof that males have a marked advantage over females in nearly all sports: "They're called world records."