Have we succeeded in building a living organism from inanimate material?
It depends on your definitions. 

we have built organisms with an entirely synthetic genome. basically the genome was "printed" from a computer file and inserted in a cell which had its DNA removed, it continued to function and replicate just fine. 

We have not built a modern cell from scratch, mostly because even the simplest living cells today need to compete with other more complex cells so they are still extremely complex in their own right. The simplest possible cells would never survive in the current world due to competition and "predations" so we don't know exactly how it has to be arranged to function.  

You may want to look at the much more modern experiments like the Urey-miller one, Jack Szostak has been trying to work up to what you are looking for, his lab has created RNA from abiotic (non-life) sources.
This is probably the closest since we know a slightly longer sequences of RNA can be self-replicating. And Harvard scientists have put manufactured self replicating RNA in an artificial lipid capsule and gotten it to function. 
 Getting the right sequence of RNA to form by itself is possible but would probably need several billion repetitions of the first experiment.