The phrase "existence precedes essence" as affiliated with atheistic existentialist Jean-Paul Sartre is supposed to refer to his notion that humans determine everything about their identity being their mere existence. Exercising freedom as individual creatures of the human species, we must, according to this ideology, construct our own identities and meaning in a life where there is no default, transcendent meaning to already cling to. In other words, humans exist, and they decide or shape their essence, their nature, across their lives. There are some aspects of this that are demonstrably true, some that are demonstrably false, and some that no human could possibly know or have known even if they are/were true.
Of course a thing cannot have a particular nature unless it exists. A person cannot be articulate or introspective without already existing in order to have those qualities, just as a building cannot be tall or unstable unless it first exists to have these characteristics in the first place. A nonexistent person cannot be introspective, for example. Yes, logical possibilities that govern real and hypothetical examples of anything at all exist independent of all else because they are logical truths, and the laws of logic both underpin and transcend everything other than themselves, but here I am talking about non-hypothetical examples of things. If a person or object really does exist, its existence is a logically necessary prerequisite to it actually having any further qualities.
Sartre does not stop here, however. He not only assumes that atheism is true--even it it was both not possible to prove that there is an uncaused cause and true that there is no deity, atheism would be completely incapable of being proven by beings with human limitations, so in either case, only a fool would be an atheist--he also pretends like humans can construct meaning in the sense of values that are truly meaningful, as if wanting something to be good or valuable (not in the sense of financial value or valuable for understanding the nature of reason, which is true whether or not objective values exist, but valuable in the sense of having moral worth) makes it so and as if the conflicting, subjective perceptions of all humans across history could possibly be simultaneously valid.
This is the typical case of someone who irrationally believes nihilism, which is an inherently irrational belief because nihilism cannot be proven or disproven by humans, even though it is ultimately either true or false, and there could be no direct evidence for nihilism short of logical proof because no amount of perception means that meaning does not exist. All but perhaps a few nihilists are too stupid to even be consistent with their total assumptions about how there is no moral obligation or meaning by insisting that, even though meaning and morality do not exist, we can actually make them exist in a binding but non-binding way by just wanting certain things to be good, evil, or objectively meaningful. Nihilists very rarely even remain consistent with nihilism itself despite it allegedly being their worldview.
No amount of trying to will values into existence or out of existence changes anything about reality except for what one is attempting to do at the time. This, too, is an error on Sartre's part. There is also the fact that in order to exist as a human, someone must have a nonphysical consciousness inhabiting a very specific kind of body, one that, despite the wide range of possible aesthetic and physiological differences from one person to the next, is bipedal, mammalian, and so on. There are aspects of being human that are neither determined by one's will nor are secondary to being human: without these traits, someone is not human at all! Even on this level, Sartre's version of "existence precedes essence" has very overt errors.
Existence precedes essence only in the sense that something must exist for it to actually be part of reality and have any further qualities. In all other regards, the ideas behind this as associated with Sartre are either easily disproven by pure reason, and thus logically impossible, or epistemologically nothing but random assumptions that could not be proven true even if they were all consistent with each other. This kind of nuance and specificity is, however, not what many people who analyze the ideas and lives of deceased philosophers tend to seek out. Here is yet another example of something that in part is demonstrably true and in part contradictory, false, and/or assumed.