@Leadfoot,
Much of what makes life an inevitability is time; even a statistically rare event approaches a probability of 1.0 when time is expanded into the billions of years. Many organic chemical reactions (required for the evolution of life) can occur spontaneously, but take extremely long periods to do so. De novo biosynthesis of the pyrimidine nucleotides uridine triphosphate, cytidine triphosphate, and thymidine triphosphate for instance takes about 78 million years. That's far too long to wait for any laboratory experiment, but a blink of the eye compared to the age of the universe. But there's likely a domino effect in organic chemistry, as for instance once the enzyme Orotidine 5’-phosphate decarboxylase (OMP decarboxylase) exists, under its catalytic effect,
the 78 million year reaction changes to 18 milliseconds.
Radzicka A, Wolfenden R (January 1995). "A proficient enzyme". Science 267 (5194): 90–3. doi:10.1126/science.7809611
Thus it's likely that nothing much happened for millions of years, then suddenly, bang zoom, no stopping us now, as organic chemicals and enzymatic catalytic reactions speed reaction times up to 10^17 fold.
As to evidence, short of waiting 78+ million years, the two most likely sources of evidence that could happen in our lifetimes (if ever) are 1) evidence of separate abiogenetic origins of life forms having evolved on earth and 2) evidence of non-earth life having existed on Mars. As I've already mentioned, (1) may be staring us in the eyes already, if it turns out that viruses evolved completely separately from cellular organisms. If you read the literature suggesting the idea of cellular biology evolving from viruses or both evolving from a common ancestor, you'll find there isn't much to go on. The fact that human DNA has many viral fragments is meaningless, since viruses are known to leave bits behind in any species they infect; that's simply
what they do. In the scientific literature this is still an open question but one with huge ramifications. It might well be that each kingdom of life will one day be believed to have its own abiogenetic roots, which when considered along with the reproducing but not-quite-life forms such as viruses and prions, could give 8 or more known separate instances of abiogenetic evolution. Given the age of the earth at about 4.5 Billion years, 8 occurrences makes it a pretty darned frequent event relative to the age of the universe.