The words "humanistic" and "existential" have a lot of different meanings, which makes this question somewhat ambiguous. But from the phrasing "humanistic/existential theoretical perspectives" it actually sounds to me like you're approaching this in terms of psychology or specifically psychopathology. There is a school of psychotherapy theory called "humanistic/existential theory" that we can draw from here. I'll just call it "humanistic" from this point because I think that's a better description and it's faster to type than the whole thing.
Humanistic psychology arose as a backlash against behaviorism, one of the earliest (and as a result, worst) theories of cognitive science. Behaviorism said that because cognition was not directly observable, it should be ignored and treated as beyond the bounds of science, and our understanding of the behavior of humans and other animals should be entirely based on the assumption that stimuli lead directly to responses. Behaviorism completely denied any concept of free will; it assumed that your behavior was completely determined by the inputs you received, making you essentially a robot that follows whatever commands it is programmed with.
Humanistic psychology basically started by saying, "Wait a minute; that's clearly not true." When presented with the same stimuli, different human beings often behave quite differently. The same person can respond to the same stimulus in different ways as they learn or change over time. Something important is going on inside the brain---if nothing else, processes like learning, memory, and emotions---which influences our behavior.
Humanistic psychology then went further, adopting a lot of concepts from philosophy that were felt to be lacking in cognitive science at the time. One of these was free will: It is a central tenet of humanistic psychology that all human beings have the free will to make their own choices and improve their own lives. Humanistic psychologists pride themselves on treating their patients as whole human beings and giving them the autonomy to choose their own paths; and humanistic psychotherapy is generally pretty effective (the most effective form of psychotherapy is cognitive-behavioral therapy which is sort of a formalized humanistic psychotherapy).
Thus, the success of humanistic psychology and the failure of behaviorism constitute evidence in favor of free will and against... well, that's the thing; I'm really not comfortable putting the bald word "determinism" there. It's evidence against narrow determinism, or greedy determinism, or stimulus-response determinism.
Because there is actually no conflict whatsoever between free will by any sensible definition and determinism. Determinism just says that all effects have causes; it could be wrong (the jury's still out on the determinism of quantum physics), but it's definitely a very good approximation. At least almost all macroscopic effects have causes.
Then we should ask, what does free will mean? That's the problem, different people mean different things by it. Some make some really strong requirement about "metaphysical freedom" or "independence from causality"; but those frankly don't even make any sense. If our behavior didn't have causes, that wouldn't make us free; it would just make us random. Dice rolls are not free will.
Instead, I think the humanistic psychologists have the right definition of free will: Free will is the capacity to make decisions. It's the capability to think about what you want to accomplish, and then form plans and intentions to accomplish it, and then actually go out into the world and try to do it. Humans absolutely do have this sort of free will, and at least to me it seems plenty good enough to justify things like personal autonomy and moral responsibility (which were really what we wanted free will for in the first place, right?).
Yet notice how this humanistic free will is completely compatible with determinism (it is in fact called compatibilism, linked below). Nowhere in there did we say that people acted without causes; we just said that their causes were based on things like desires and intentions rather than simply being meaningless particle interactions.
Now, the really hard part is that we are made of particle interactions; the trick is to realize that we are not meaningless particle interactions. Not all particle interactions are created equal. When particles get together to form something with the complexity, computational power, and above all capacity for consciousness that human brains have, they attain a special status. If this seems weird to you, consider that a table and a glass of milk are not the same thing, even though both are made of protons and electrons. Being made of particles isn't the same as being just particles. The arrangement matters.