How do I identify the fermentation process in a wild ferment?
In addition to @kitukwfyer's answer. There's quite a bit of biology that goes on here...
Not only are you influencing the competition, you are actively selecting for organisms that grow well under the conditions. This is the real reason brewing (and bread etc) works better with a starter culture. There are a few things influencing this:

With a starter culture you are putting in a high number of organisms, which results in a shorter lag phase. Wild ferments rely on a relatively low abundance of naturally occurring organisms - so have a long lag.
With a starter culture you are also adding organisms that are already at least semi-adapted to the type of culture, so they will grow better.
It takes a while for the wild organisms that are there to actually adapt to the conditions. These are related to abundance of water, salt(s), nutrients, oxygen, CO2, pH etc; all of which may be on the boundaries of what is tolerable for the organisms that are there. Cultured organisms are at least partially selected for these characteristics already and selected against ones you don't want, indeed that is actually part of the reason people add things like acid to fermentations - it inhibits gut microflora like Escherichia coli that can make you quite ill.
In the ferment you are selecting for strains that grow well under the conditions; this will be a small proportion of those that are there, so it results in a very small inoculum, and a long lag phase.
Finally, wild organisms often have slow growth rates compared to cultured ones, because we generally want things quickly, so we select for strains that grow faster under the conditions we want - you probably did this subconsciously a couple of times already - you didn't see any signs of fermentation in a brew, so you threw it out and made a fresh batch; or something along those lines.

As to how you can identify the organisms - your best bet would be to get or make a bunch of bacterial (aim for lactic-acid fermentation ones here) and yeast plates (use some filter sterile fermentation broth as the liquid base if possible) and start streaking out your cultures. You most likely won't be able to culture all the organisms in your ferment, but you probably can culture those with the highest abundance (you already know they grow well under some conditions). You can then pick off individual colonies from our plates and grow them in liquid culture to see which have characteristics (flavour profiles) you like by themselves or in combination (try smelling them before drinking...). This is not a trivial task (list of techniques you might need) and relies on a bit of good sterile technique and a knowledge of what a &quot;normal&quot; organism looks like, not a contaminant from your own microflora.