This is one of the great mysteries in Science and I think it is more complicated than most people realize. Here are the basics as we currently understand them:
1. All life on Earth on a molecular scale works in almost the same identical way using almost identical processes, proteins, enzymes and other molecules such as DNA or RNA
2. These molecules are not simple, they are extremely large and complex. The notion that randomly mixing the right types of atoms will somehow produce the complex protein molecules of life is like suggesting that stirring up a kettle of sand, metal filings and dirt will spontaneously produce a computer.
3. Our study of the fossil record of ancient species and the DNA of extant species both show that all living things are connected in a "tree" structure that stretches back in time.
4. All living things come from other living things (as far as we know.) In other words, there is NO evidence anywhere in the world today (that has been found) of a process where a living thing can somehow arise from nonliving things, nor is there any fossil evidence of such a process happening in the past.
What this indicates is that the dawn of life was a singular event in Earth's history. Whether this was the emergence of some "thing" from deep inside the Earth, under the sea or outer space, we have no idea. At least not yet!
Several posts have proposed the "Panspermia" theory as to the origin of life on Earth; it's very difficult to determine when the origin occurred, as we have yet to define what life is, exactly. We may get a closer definition and a deeper understanding once life is found outside of Earth. As more and more extrasolar planets are discovered, this seems inevitable. We may even find it in our own Solar backyard -- Europa, a moon of Jupiter, has lots of liquid water -- something that would lead us to consider finding something like what we would expect to be life:
I agree that this question probably cannot be answered definitively, at least not with the knowledge we possess at present. Some of the proposed theories are more persuasive than others, but we will probably need to find life somewhere else before we can begin to feel confident about how life arose here.
I, too, think that you are going to receive many different answers on this. I tend to believe that we simply do not have enough information to make a distinct "ruling" on this. While we have many different suggestions (God, Big Bang, Intelligent Design), there is not one which proves to be evident beyond a doubt. I simply think that this is one question that will never have an answer which makes everyone happy.
One of the major scientific theories holds that the basic building blocks of life got to the planet when it was hit by comets and such. Of course, this still does not get to the ultimate question. No matter how life arose on Earth, we still we be left not knowing how the universe got here in the first place. And so we end up with a theological question once we get "under" all the science.
You are far from the only individual who would like an answer to that question. Unfortunately, there is no one definitive and all-inclusive way to respond. As suggested by the previous posts, many religions have explanations based on the beliefs of those religions and expressed through the writings, based on oral retellings, based on the experiences and interpretations and legends passed down through human history. Scientific explanations based on finding of fossils and DNA testing and other artifacts provide links and connections and tantalizing gaps that have yet to be explained.
There is some evidence to suggest that life originated with bacteria in the depths of the ocean and evolved from there into all the species of sea, land, and sky. As for the religious aspects of the origin of life, every religion has its own "story" on this. I understand that some people have faith in these stories, but they vary considerably amongst religions, and I have a difficult time subscribing to the notion that one of these narratives is correct and all the others are incorrect. That would imply that there is only one religion that has the answers, only one true way, and I simply do not believe that is the case. If one believes in a higher being, then surely there are many paths that are righteous.
Unfortunately, I don't think you are going to get everyone to agree on an answer here. There is a religious answer, God created man, and a scientific one, life originated with the Big Bang. The truth is, that's not really specific enough. We just don't know.
By pure good fortune I have just found an upload on Youtube of a truly brilliant, user-friendly series from The BBC called 'The Cell'. It is a brain-popping, 3-part documentary about cells and their function. I'd truly recommend you watch the whole series (three hours very well spent). The link below is to the 3rd and final episode and it focuses on abiogenesis, the origin of life. It is not an 'unfathomable mystery', it is bio-chemistry.
Also, there is of course the wonderfully fun theory that the original organic materials that started life on Earth were extra-terrestrial. It may sound a bit 'woo-woo' but we have found various organic chemicals (NOT life) in space. And it is possible that Earth's original organic material travelled here on a piece of space debris which crash landed into a suitable environment, e.g. a hot spring.
You have to remember that the time scale for these events is billions of years. So even if it sounds very unlikely, given enough time it becomes perfectly possible.
It's a difficult question and we may never find the exact answer; we're talking about a few molecules billions of years ago, after all. But we have a pretty good idea of how it probably happened.
The first thing to understand is that the first 'life' wasn't a cell or even a proto-cell, it wasn't even life; it was simply basic, organic chemistry. The big trick is making the first organic chemical that can make a copy of itself from its surroundings (replication) There are lots of candidates for this role, eg amino-acids. They can form purely chemically and can join together to more complex molecules. You then wind the clock forward millions of years as these bio-chemicals develop in complexity and co-operation. They are still not truly living things though. Probably the nearest thing today that resembles these early life forms are viruses. In fact many biologists do not consider viruses to be truly 'life' but merely self-replicating organic chemicals
There was a famous experiment in the 50s called the Miller-Urey experiment that demonstrated that you can persuade inorganic chemicals to form into organic chemicals. Here's good old Carl Sagan giving a 5 minute summary of the chemistry of life's origins; enjoy.
(P.S. A couple of posts refer to the origin of life on Earth as the Big Bang. The Big Bang is how the Universe started. The origin of life on Earth is called Abiogenesis. :-)