Big wall of text incoming. I highly encourage you and others to read through it all, and I'll also provide supplementary images and video at the end to help give extra context and understanding.
So to start off with the soul, in order to prove its existence, you have to first define what a soul is and how it can exist using physics and metaphysics. To do this, you must have an understanding of how the fundamental laws of the universe work with matter through the study of physics and metaphysics. A soul is defined as an incorporeal or ethereal essence or consciousness inside a living being. Souls are said to inhabit things that are biologically alive. The definition of being alive, or life in general, is anything that distinguishes a vital and functional being from an inanimate organism. (Also side note, the word soul comes from the Greek word "animus", which is where the word "animated" comes from, anything that is animated is considered to be in motion.) And on the inverse of life, the definition of death is the biological termination of the vital processes that sustain a living organism. Typically, a death is acknowledged and recorded when the neuroelectrical signaling process of an organism stops. So then, death would be considered as a state when there is no more electricity being conducted through a body.
Now, electricity and magnetism are the two fundamental forces that dictate the form and shape of all states of matter. All matter is comprised of atoms, which are the smallest measurable unit of matter we can use, and they are made up of three sub-units called protons, neutrons and electrons. Protons carry mass with a positive, masculine and repelling electric charge. Electrons carry mass with a negative, feminine and attracting charge. Neutrons carry mass with no charge. These 3 sub-units of matter are then used in many different combinations to formulate different elements and compounds of matter, such as hydrogen, oxygen, carbon, and nitrogen. (Ironically, these are the 4 elements that are comprised of DNA and are the blueprint for organic life.) In order for the atoms to take on different combinations, they require different amounts of energy and radiation from the electromagnetic spectrum to affect their polarity, or electric charge, and they will either repel or attract different atoms.
The electromagnetic spectrum consists of varying levels of wavelengths, frequency and vibrations of energy and radiation, which take on the form of different wavelengths of lights and sounds. Photons are what exist at the epicenter of electromagnetic waves. They are very small light particles that carry no mass, but always move at the speed of light even in a vacuum. Information is encoded into light and sound, and thus they can be recorded to affect different states of matter at different frequencies. Light can be used at different wavelengths to grow plants in greenhouses a certain way, or to see objects that are normally not visible under regular circumstances, such as urine stains in ultraviolet light. Sound can also be used at different wavelengths to generate different feelings of emotions, or to give geometric shape to a form of matter that is otherwise normally formless, such as putting a drop of water into an acoustic chamber, and different harmonic levels of sound will produce different star shapes in the droplet. So therefore, light and sound can be used to alter the state of matter by energizing subatomic particles in order to induce a certain electric charge.
Consciousness is ultimately defined as the state of awareness that an object has of its surroundings. Typically, consciousness is denoted with living organisms and their reactions to the five physical sensations in the form of touch, sight, taste, hearing and smell. Again, in order for something to be alive and conscious, it requires electricity to be conducted through the body. We have proved that electricity can be found in atoms and other subatomic particles, and we proved that they react to different levels of electromagnetic energy and radiation. Therefore, atoms are a form of sentient and conscious matter, and their collective consciousness together allows them to formulate into different and more complex patterns of matter. Therefore, anything that is comprised of atoms at the lowest fundamental level of measurement and observation is by definition alive and conscious. All physical matter is made of the same elements, therefore all matter is interconnected consciously at the subatomic level.
Now remember that energy and radiation from the electromagnetic spectrum is comprised of photons that have no mass and can move at the speed of light, even in the vacuum of space. In the electromagnetic spectrum, we use hertz to measure waves. A hertz (Hz) is the frequency, or how many times, a wave vibrates in one cycle. Think of how many times you can beat a drum in a second. One kilohertz (KHz) is 1000Hz in one second. One megahertz (MHz) is one million Hz. One gigahertz (GHz) is one billion Hz, and one terahertz (THz) is one trillion Hz. Our sun, for example, is made of an exponentially huge amount of atoms, and is essentially a giant ball of electricity and magnetism. In order for the color red, the first color of visible light, to manifest and become physical, the sun has to be generating energy at around 4.32 10^14 Hz, or 432 THz frequency. That's 432 trillion times in one second, and the sun could fit about one million Earths inside of it. Give the size, that puts into perspective how powerful stars truly are. Thus, the sun is essentially a supermassive collection of consciousness, information and energy that is vibrating trillions of times every single second. But as we all know, as with all things that exist in life, even the sun itself has an expiration date.
Moving forward, all matter is temporary, because all matter is made of atoms, and atoms are bound by the physical laws of our three-dimensional universe. However, the soul is immaterial and cannot be directly measured by the tools of our current three-dimensional universe. Therefore, we can state that the soul is not bound by the same fundamental laws of the universe that physical matter is. This is evident with our observation of photons, which are information-encoded light particles that have no mass and can travel at the speed of light. However, we do know that things or beings that are immaterial can have a indirect (or sometimes, direct) affect on physical objects or beings in our material plane or three-dimensional spacetime. Again, we know that photons, or light + sound information, can be physically experienced and felt in our bodies. When we listen to different kinds of music, we can feel the vibrations resonate with us, and it can affect our moods. We also know that we cannot visually see things that are outside our immediate perception of visible light, but they are still existing. We can see things that are normally rendered invisible to our eyes with the aid of infrared or ultraviolet technologies.
---
"A man who stands for nothing will fall for anything." -Malcolm X "Truth, Freedom, and Health." -V.A. Shiva