If the Big Bang wasn't brought into existence by free will, then there must (not necessarily) be an infinite regress of preceding causes that led to up to the Big Bang.
Given an infinite amount of time (nothing could ever happen, XENO'S PARADOX), any action that has a greater than 0 chance of occurring will inevitably occur.
One this action inevitably occurs, we can count backwards the number of trials that led up to the action (only if those "trials" are verifiable using logic based on verifiable evidence). By doing this, the entire event has a quantifiable beginning (only if it is verifiable).
The problem is that given an unlimited amount of time, something that can happen inevitably will (and yet, at the same time, nothing can possibly happen). This gives you an infinite chain of events (there can never be an "infinite" anything, much less a "chain of events") that all have quantifiable beginnings (only if they are verifiable) to them which is logically absurd. The only (not the only) way around this is if an action occurred by free will (free-will is a human EMOTION, not a logical necessity or a verifiable fact) - in that case the event will not have a quantifiable beginning (if we cannot verify an event with logic and evidence, it cannot be quantifiable).
Either A "chance" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or B "physical, verifiable causes" - VERIFIABLE, can be eliminated as a primary factor (logically), but not as a potential secondary or tertiary (or potentially hundreds of bobaquinchillions) hidden variables, has no explanatory power, indistinguishable from either random or no explanation
Or C "the human emotion we call free-will" - UNVERIFIABLE scientifically, logically FALSIFIABLE able to eliminate this as a conceivable option (maybe a human caused the cosmos with the aid of non-linear-non-local causality), has no explanatory power, indistinguishable from either random or no explanation - If FREE-WILL is a hypothetical primary cause of the cosmos, FREE-WILL itself must be "uncaused" and would therefore be indistinguishable from random
Or D "quantum flux" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or E "noumenon" - VERIFIABLE, can be confirmed as a primary cause (logical necessity) and has zero explanatory power, indistinguishable from either random or no explanation
Or F "we have no flipping idea" - VERIFIABLE, and yet has no explanatory power, indistinguishable from either random or no explanation
Or G "dark energy" - Indirectly VERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power
Or H "magic" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or I "Nanabozho" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or J "Marduk" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or K "Zeus" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or L "Pangu" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or M "Brahman" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or N "pure imagination" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or O "eternalism" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or P "string theory" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
Or Q "M-brane theory" - UNVERIFIABLE, UNFALSIFIABLE unable to eliminate this as a conceivable option, has no explanatory power, indistinguishable from either random or no explanation
I'm sure you get the idea.