Although science cannot prove a miraculous intervention, science can assess the probability of a natural cause.
The situation: There were a few simple worms, simple invertebrates, and small shelly fauna, at the beginning of Cambrian. Then, at the time of the Chenjiang Lagerstatten, 517 Ma, the vertebrates appear along with some amphioxus like animals (headless, brainless, sightless, boneless). DNA evidence shows that the vertebrate DNA is derived from amphioxus DNA. So, the evidence indicates that vertebrates descended from an amphioxus-like animal, which evolved in the early Cambrian. Vertebrates are deuterostomes, and no other deuterostomes appear in the fossil record before 517 Ma. I believe that a recent paper indicates that the interpretation of sea squirts (deuterostomes) in the fossil record of the Chenjiang at this time is incorrect, but I don’t want to go into this here.
The first vertebrates (517 Ma) were lampreys. The early vertebrate brain has millions of neurons whereas amphioxus had thousands of neurons. The following features were not in amphioxus or any other animals of the early Cambrian. The vertebrates have an internal skeleton with a unique head with braincase, mouth, and two eyes, branchial skeleton surrounding the gills, cartilaginous pipe. Neural crest cells, unique to vertebrates, migrate from the neural crest, along the nerve cord, and leave the nerve cord at various locations in the body, triggering the formation of different organs. These cells form the bones of the chest, the head, the ears and other sensory organs, the skin and pigmentation of the skin, teeth, and depending on the vertebrate, scales, feathers, or hair. Other features formed by the neural crest cells include adrenal glands in the kidneys that produce hormones, neurons in the central nervous system that connect to the peripheral nervous system (spinal ganglia), intestinal tract nervous system that governs gastrointestinal processes, and some of the blood vessel sections. The lamprey had a fully developed vertebrate eye whereas amphioxus only had light sensitive eyespots rather than eyes. Henry Gee described the unique features of the vertebrate nervous system, many of which were in place in the original vertebrate fish. The olfactory bulb communicates smell to the brain through the amydala, in lampreys and in humans. The pituitary gland (hypophysis) controls appetite and sexual arousal through MSH. It also regulates reproduction, growth, and stress. All vertebrates have olfactory, optic, oculomotor, trochlear, trigemal, abducens, facial, auditory, glossopharyngeal, vagus, accessory, and hypoglossal nerves, but invertebrates do not have these nerves. The myelin sheaths that encase vertebrate nerves are an important part of the nervous system. Mylenated nerves cause impulses to jump from periodic breaks, and travel 100 m/sec. Loss of myelin causes loss of function because signals travel at least 100 times slower. Interestingly, the genes for myelination are found in lampreys even though they did not have myelin sheaths or myelin. It seems that the genetic code for producing myelin was in place before the appearance of myelin. The vertebrate closed blood vessels are lined with endothelium, which is unique to vertebrates. Endothelial cells give unique filtration and signaling capabilities to blood vessels, enable scabbing (hemostasis), aid in the immune system. The chambered heart is unique to vertebrates. The vertebrate kidneys control a water management system that is unique to vertebrates and allows them to live out of water. Vertebrate sex organs are uniquely controlled by hormone signaling. The vertebrate acquired immunity system (antibodies) is particularly remarkable. The vertebrate kidney was an important feature for the eventual migration of vertebrates to land. It regulates salts, the acid-base balance, and electrolyte concentrations. The kidney removes salts, ammonia, and toxins in urine. It also controls fluid levels in various fluid compartments in the body and filters one-fifth of the blood volume that enters the kidneys. The kidney is not in any invertebrates. The vertebrate adaptive immunity system is highly complex. Plasma cells form specific antibodies designed to attach to specific types of pathogens. This triggers a series of enzymes called the antibody complement system that actually drill a hole in the wall of the pathogen. Helper T cells recognize foreign matter and communicate that information to the immune system. The vertebrate Hox gene system is basically 4 times for complex than invertebrate Hox genes.
There is a reasonably good fossil record from the Ediacaran Period prior to the Cambrian. There is no evidence of any of the vertebrate features in the Ediacaran or in the early Cambrian. What is the likelihood that all of the features of vertebrates formed along with and after amphioxus between 542 and 517 Ma? DNA molecular clock scientists calculate time spans like 100, 200, or 400 million years for the formation of the vertebrates. Yet, there is no evidence of any evolution between amphioxus and vertebrates in the fossil record prior to 517 Ma.
If you want to believe that God never intervened in the universe and that the evidence for vertebrate evolution is hidden somewhere in the rocks of the earth, then that is up to you. However, please do not criticize the belief that God intervened and formed the vertebrates because you have no data to support your position.