I'm a scientist, but not in astrophysics or a (remotely) related discipline.
At some deep level, I "doubt" the big bang theory because it seems to me that it is not something that can really ever be tested, simulated, experimented with, so we have n=1 observational data at best, and building causal theories on n=1 observational data is tricky; and on another level I "doubt" the theory because I don't know the literature or even really understand the phenomenon and I have no clue what the scientific evidence for and against it are. "They" say that it is the currently accepted theory, but what does that even mean? Why would I not doubt it?
All that said, I don't believe that the theory is false, I just accept that "other scientists" know what they are doing so as a body they are probably right if they accept a model. But I don't like accepting things on authority, I like understanding why something would be the case, and I don't have that understanding for big bang theory.
[at least with other "grand theories" like tectonics or evolution I have some understanding of the process involved and the evidence that lead the scientific community to accept it (e.g. the magnetism 'bar code' for tectonics) and it can be observed somewhat in real life (the functioning of current species, the shape of continents. And let's not even talk about flat earth, young earth, intelligent design and other complete hogwash]