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Empirical observation can get you the what and the how, but I don't think it will ever tell you the why. Who says there even is a why?
The difference between "how" and "why" doesn't seem very meaningful to me. For example- why does water boil? It boils because molecules gain enough energy through heat to transition states.
In that same sense, OP's question
There's a non zero chance that we eventually understand the mechanisms behind the big bang and can explain how nothing turned into something. Therefore we will be able to explain the why, no?
The problem with the question of why is that you can always ask why again. Say we do understand the mechanism of the big bang. You can still ask "why" about why things are that way. Which is why in my view that's still more of a "how?" "Why" is more of a question for philosophers than scientists imo.
But is that not the same way with "how"?
How do objects fall to the ground? → the Earth exerts a gravitational force on them
How does Earth exert a gravitational force? → All objects with mass create a gravitational field that attracts other masses
How do objects create a gravitation field? → Mass warps spacetime and this curvature directs objects to follow paths towards the source of the mass
and so on, etc
I think the "why" exists only with the idea that the universe is directed in some way. e.g. "How can I see around my room"? Photons. "Why"? Because I turned on the light.