There are an infinite set of solutions to any problem but there may only be one that is right. With many maths problems the answer can be proved but with physical problems, none can be proved, only disproved. All that can be done is look for a theory that is self consistant, consistant with the rest of physics, and able to make valid predictions. Another general rule that is applied is that it should be the simplest solution. It is usually easy to (say) arbitrarily add another term to an equation (or otherwise modify it) that plays no part in any measurement capable of being made. Of course, if someone had (without justification) suggested to Newton the equations of special relativity, it would have been a very, very lucky guess and would have probably been dismissed as mad. But this is not really the way science works and it never happens like this.

There are other principles that can apply, particularly in cosmology, but that are not always accepted by all. The Copernican principle and Anthropic principle are two examples. Not accepting one or more of these principles opens up huge realms of other possibilities but it does not get us any further in undersanding.

I'm afraid modern physics is not really very open to the non-specialist like it was (maybe) in the days of Galileo. Most of us struggle with our own narrow fields and there are few true polymaths around. There are plenty of disagreements in physics but to get an appreciation of these I think it is necessary to spend a long time studying and understanding the details. What is popularly presented (certainly in cosmology) is very simplified and the most accepted basic concepts. But this is because trying to explain ideas like Riemannian spaces and differential geometry on a TV programme is not a viable task.

Conventional wisdom is more than likely not right but it is probably the best we have. If you wish to overturn ideas then there is quite a large amount of justification rightly required.