Reproducing the Miller-Urey experiment may be fun but it would improbably bring new science. They obtained amino-acids, you would too. But before obtaining a living cell, you would need a full ocean and half a billion years - if it really proceeded like this.
The "analytical part" of your proposal needs more thoughts. "When the equipment recognizes a precursor" seems to suggest recognizing individual molecules, and even patience wouldn't make any macroscopic amount from molecules. Also, most analysis equipment destroys the molecules to recognize them. You have to restrict to some processes like chromatography.
You might want to consider my old proposal to make micro-sorters by semiconductor technology. I meant them to separate sick blood cells, they could separate individual molecules in amounts less tiny than otherwise. Integrate 10
4 actuators per chip, put 10
6 chips in a machine, let them operate in 10
-2s over 10
7s, and you have processed 10
19 elements, of which you keep some. Still not a mole, but already in the µg region. You need some distinctive molecular property that the actuators can recognize easily and quickly, like fluorescence.
In the same spirit as Miller-Urey, I'd like to suggest the random production of cage molecules, in amount sufficient to study their properties. Take a broad mix of alkenes, allenes, alkynes, polyenes... and inject atomic carbon among them, for instance by sublimation of carbon after diffusion through tantalum
https://en.wikipedia.org/wiki/Atomic_carbonhttps://en.wikipedia.org/wiki/Phil_Shevlinor by one of the untested methods (= risky lengthy) I suggested there
http://www.chemicalforums.com/index.php?topic=72951.0