This idea of being able to draw a line in the sand to say, everything on this side is life, and everything on the other side isn't, is either arbitrary or impossible with our current understanding.
This is because the most parsimonious explanation for the origin of life is abiotic. That means, sometime in the history of our planet, things that weren't life gave rise to things that were. Earth chemistry somehow became biochemistry, as organic molecules were formed, reacted with each other, enclosed the reactions in some finite space, and started making more of themselves.
It might turn out in the end that life has some other origin entirely. However, even supposing life hitched a ride to Eath on meteors, or that aliens planted it here, that only throws the question of life's origin into an environment we know very little to nothing about--space, or other planets. So if we're going to theorize about the abiotic origins of life, we might as well make it easier on ourselves and stick with our home planet. (To get away from an abiotic origin of life, you pretty much have to suppose a Creator without its own abiotic origin, which is fine with me but gets away from the point. I'm willing to talk about it later.)
So, assume an abiotic origin of life on Earth. The development of what we can agree is life (say, a frog) from what we can agree is not life (say, a rock) was probably not instantaneous. The rock did not jump up one day and say "Hey guys, check it out! I'm a frog!" Molecule after organic molecule had to be created from other, simpler chemicals. For decades people have been doing lab experiments with conditions similar to the imagined early earth, three or four billion years ago, to see what kind of molecules they can make.
The textbook example is the Miller-Urey experiment, in which a couple of guys stuck together a bunch of glass tubes and beakers and threw in some gases that everyone's pretty sure were around on the early Earth. Then they hit it with a lightening equivalent and observed the accumulation of very organic-looking brown goop. Turns out you can make a lot of amino acids this way--the building blocks of proteins. Very promising.
Since then, people have come up with more elaborate scenarios and done nifty things with chemistry. The point is, there's no reason to think there was a definitive timepoint which marked life's beginning. But, quite understandably, everyone always wants to know when it is anyway. The whole thing is frustrating--like not knowing your birthday.
Most textbooks, somewhere a page or two before or after the Miller-Urey experiment, put the first evidence of life on Earth about 3.5 billion years ago, based on putative* fossils from rocks in Warrawoona, Australia. However, there has been a LOT of controversy over those fossils. It seems like they're pretty definitely some kind of organic remains, but papers have been published arguing that the structure and content of these remains could be produced abiotically--in fact, people have even produced similar-looking fossils in the lab.
If you're going, "Hunh? So what's the controversy?" right now, we're on the same page. If not, let me explain. Everyone thinks life is supposed to have an abiotic origin, right? So shouldn't the earliest fossils also have an abiotic origin? Shouldn't this paper proving that such fossils can be produced abiotically in the lab be used as more evidence for how life could have evolved, not for shooting down other people's arguments about early fossils?
Scientists, just like everyone else, like to argue a lot.
That said, and to be fair, the fossil record is so poor in general, and so extremely poor that far back in history, it's unlikely that the earliest life actually left us any traces by which to find it. It's quite probable that by the time we're finding fossils, life had reached the point where, had we seen whatever made the fossils, we would all be able to agree, as with wiggly little worms, that it was really life.
* This is a killer word. It makes your ideas sound a lot surer and more scientific than if you just say, "supposed."