Hardly blindly, and clearly not a priori as in your case. The hard evidence for the evolution of primates from fish is, for one with even a cursory education in the facts, a well blazed, clear trail.
For example, the recurrent laryngeal nerve.
The left recurrent laryngeal nerve (RLN) branches from the left vagus nerve near the heart, and the right RLN braches off a bit further up from the right vagus nerve. The left RLN loops under the ductus arteriosus, and right RLN loops under the right subclavian artery. They both then travel up into the neck to innervate the larynx and its surrounding muscles. Both of these recurrent paths are quite inefficient in mammals; adding over a foot of unnecessary length to the human left RLN. This is especially true in giraffes, where the added length is absurd—more than fourteen signal-slowing, energy inefficient feet are added to the left RLN alone. This data doesn’t fit the model of creation, as it would be easier and more beneficial to simply branch the RLNs off higher on the vagus nerve and avoid arterial looping completely. The evolutionary model, however, is a precise fit; especially when one considers fish anatomy. In fish, several branches extend from the vagus nerve, each looping around arterial arches that connect the dorsal and ventral aorta between each gill slit (
Ridley, 2004, p.281-282; Berry & Hallam, 1989, p.83). This is powerful evidence that mammals and fish share ancestry, that the RLNs and ductus arteriosus are remnants of the vagus nerve branches and sixth arterial arch in those ancestors, and that the configuration in mammals is a vestige resulting from decent with modification.
For example: gonads.
The gonads of sharks, other fish, and even humans develop in same place—the chest. This works well for sharks, since they stay there, but in human males, the gonads need to travel all the way down into the scrotum to keep cool. This causes an unnecessary looping of the spermatic cord, which causes a weakness in there body wall, leaving them prone to developing a hernia (
Shubin, 2009, p.64-66). This is consistent with decent, with modification, from an ancestor we share with modern fish
For example: phrenic nerves .
The path of the human phrenic nerves begins at the base of the skull, and goes through the body cavity to the diaphragm. This is an efficient path to amphibians’ gills, which are in the neck, but is an inefficient path to the diaphragm, in humans. The irritation of these nerves—made likely by their placement—can cause problems with breathing, including hiccups (
Shubin, 2009, p.66-67); a reflexive vestige.
With thanks to:
Vestigial Evidence - Evidence for the Evolutionary Model