But, according to the conventional scientific wisdom, that happened randomly.
I think your problem here is a misunderstanding of the nature of probability. If a particular event has a very low probability, but the conditions under which that event might be observed are repeated a very large number of times, then the event becomes highly probable. For example, the chance that you will throw snake eyes with two dice is only one in thirty-six; but if you throw the dice a hundred times, the probability that one throw will be snake eyes approaches one. In fact, it is extremely improbable that, throwing the dice a hundred times, you will not throw snake eyes once. Likewise, just because the chance that the particular chemicals in a flask will form an autocatalytic set in a short period of time, and in this case, "short" could mean a hundred years, is low, does not mean that the chance that one, or even many, autocatalytic sets will form in a billion years in all the world's oceans is low; in fact, because of the enormous volume involved, and the enormous amount of time, it is all but certain given what we know now that many such autocatalytic sets will form; perhaps even many billions of such sets. And, in case you missed it, an autocatalytic set is capable of reproducing itself from the surrounding material; this is the most important characteristic of that which we call "life."
Don't you think there is a rather major difference between something happening randomly and the best scientific minds using the best equipment replicating that random event?
That depends on the design of the experiment. If they were using complex chemicals, or unusual procedures, then I might agree; but they were using very simple chemicals, specifically, water, ammonia, methane, and carbon dioxide, and doing nothing but heating them and subjecting them to ultraviolet light and sparks to simulate lightning. These are a pretty good duplication of the conditions that obtained on the early Earth, and there is little room for any sort of "engineering" or manipulation; anything that happens in such an environment, particularly if it is small and only allowed to run for a short time, must surely have been duplicated a trillion trillion times in the enormous volume of all the world's oceans over the enormous time of a billion years.
And you're still stuck on the whole probability thing. You need to think about what "random" means in this context very much more carefully. For example, it is a random chance (and a very small one) that any given uranium atom will decay in any given second; the half-life of uranium is about four billion years, which means that in four billion years, there is only a 50/50 chance that a particular atom will decay; how many seconds is that? And what, then, is the chance of the atom decaying in any given second? Yet, in a relatively small volume, a few cubic centimeters, enough of them decay in a second that it makes the uranium radioactive, and strongly enough so that it will injure you if you are exposed to it for long. And even in that small a volume it is incredibly unlikely that a second will pass in which not a single atom of uranium decays, despite the incredible unlikelihood of any single atom doing so.
If you say no, why was it so easy for the Urey-Miller experiment to create amino acids?
Because the nature of the atoms in the four ices (water, ammonia, carbon dioxide, and methane) is such that they will combine in this manner and form these compounds under the conditions that obtained in the Urey-Miller experiment, and on the early Earth; their bonding strengths and angles, and the probability with which they will bond, and how those strengths and angles change when they are already bonded and encounter another already-bonded molecule, dictate how they will combine and what compounds they will form when they do so. And these characteristics, in turn, depend upon the characteristics of the electrons, protons, and neutrons that make up the atoms, the forces that bind them, and the nature of spacetime. And to top it all off, some physicists hypothesize that the characteristics of these particles and forces are also matters of the geometry of spacetime; and they have some pretty strong evidence to support this view, which is referred to as "string theory." And it is even possible that it is impossible to form that which we call a "universe" without it having this particular geometry, although that hypothesis is much less supported than the hypothesis of the geometry of spacetime determining the characteristics of the particles and forces.
And, are you aware that, following that experiment, there was great optimism in the scientific community that the creation of life in a laboratory was just around the corner?
I am not aware of any such optimism in the "scientific community," although I am aware of a certain amount of hyperbole in the popular press. I do not think that you can produce anything but speculations on the part of a few scientists, far less definitive and far less optimistic than you or the popular press of the time claim. And in any case, why should it matter? It appears the situation is far more complex (and I mean that word in all senses- an entire new branch of mathematics has had to be created to describe it, and the name of that branch is "complexity theory") than was appreciated in the 1950s. Is this so surprising? For life to be so difficult to quantify and understand, it has to be complex and embody elegant and counter-intuitive principles, just as physics does, and even moreso. Why, then, should I or anyone be surprised that the 1950s understanding of life should prove to have been as far or farther from reality as the 1950s understanding of physics? Is it not both hyperbolic and essentially disingenuous to make such a claim?
Can you specify a rough timeframe for when this will actually happen?
No, can you? How about you specify the rough timeframe for when we will know whether string theory is correct or not. Can you specify that? How about when we will reach Mars with a manned mission? Or when we will cure cancer? No? Well, then, why should I be able to predict when we will understand life to that level? And why should it be proof that we will not if I cannot?
