If you cannot accept BBT then what do you accept?
The problem is with the word "accept".
What I "accept" is that a lot of work has gone into trying to make sense of experimental observations and astronomical evaluations, and that some people have developed a consistent set of mathematical descriptions that quantitatively account for those observations. I also realize that those mathematical descriptions involve a lot of assumptions, "tuned" parameters that were adopted on the basis of speculative conjectures about how things might work, and multiple "puzzles" and "paradoxes" and "dualities" that still can't be explained, but are just "accepted" by the modelers as inherent aspects of their current way of thinking about the observations and/or predictions for which there are no available observations.
What I don't "accept" is that unverified predictions must be correct, just because the "best" current model made those predictions. But the commercial media loves to print statements like "The whole universe started 13.8 billion years ago as a tiny spec that suddenly grew at speeds much faster than the speed of light, transforming pure energy to the matter that we see today," as if those are proven facts rather than the mathematical extrapolations of models that have some real problems with their verification.
I understand that the communication media companies will always seek to sell their wares by including "shock" in their advertisements. But, I do not like to see serious scientific discussions lose their connections to the bedrocks of observations and start suppressing thinking that does not adhere to the "best" model of the day. Even the best models of today are clearly not good enough in many respects, and people are working on improving them in many areas. In my opinion, we need to keep in mind that we might need some substantial rethinking of some fundamental concepts, not just small "tuning" modifications to make existing models continue to match each new observation of quantum level or cosmological level phenomena.
My person manner of thinking about scientific models is related to the level of confidence that can be developed in their structure, or alternatively, the uncertainty level associated with their structures. Unfortunately, there really is no complete process for estimating the total amount of uncertainty in a model or theory. So, I tend to think about known contributors to that total, without expecting to be able to even compare models on the basis of their respective totals.
In that way of thinking, the BBT has a lot of substantial contributors, or maybe I should call them "red flags" to its level of confidence that it has not gotten something substantially wrong. We have already talked about only having observed 5% of the matter and energy assumed by the model to exist in the present universe. And, we have astronomical observations that take us back only to about 6.4 billion years ago (assuming that the BBT is correct to back at least that point in time), leaving all previous times unobserved and conceptualized on the basis of quantum theory. But, we have no actual experiments of the conditions that we postulate to occur in the highly compressed universe before that time, and are inferring them on the basis of proton-on-proton collision debris observed in atom-smasher experiments, which involve the interactions on only pairs of protons per interaction, not a universe's worth of matter all interacting simultaneously in extremely dense configuration.
So, my personal confidence in the BBT before 6.4 billion years ago is very low, and even after that time, I am open to other interpretations of the the currently available observations.
That doesn't make me "ignorant" or "stupid", although I am surely not as knowledgeable about the intricacies of the specific models as are those who developed them or even studied them as coursework for their college degrees in physics or whatever. I just have a somewhat different focus on the models, thinking about how much is actually verified as my top priority, rather than having a top priority to make the models work with each new observation.
Although I have been a "modeler" in my past employment, I was also used as a reviewer, so I tend to think of other people's models as a reviewer, rather than as an implementer. As a reviewer, I not infrequently found errors that had the character of being suitable for use in the situations where the model was tuned and intended to be used, but still resulted in bad predictions and wrong conclusions when applied to substantially different situations.
Although it is clearly not exactly the same thing, it is that type of limited thinking applied as a quantitative model to normal operations that led to the operating crew at the Three Mile Island Nuclear Power Plant misinterpreting their instrument readings, thus taking the wrong corrective actions during an off-normal situation, and ultimately letting the reactor core in Unit 2 overheat and melt back in 1979. That is the problem with not being able to think "outside the model" sometimes referred to as "the box".