1. Science is a highly specialized field that is done by experts. You can't really understand science without having gone through the process of study and practice. This is a strength of science.
I agree. The problem is science proposes matter can just pop into existence at the high energy, conditions of the early universe soon after the Big Bang. The problem is it takes matter interacting with the space time continuum (higgs field) for a gravitational field to exist and, there was no matter before the Big Bang. So, how did gravity drive the Big Bang and matter.
2. One you go through the process of learning the math and studying past work, everything in science is testable and repeatable.
The Big Bang is not testable. We understand the past by looking at the information that has been stored in matter and the structures of the universe since the ancient past and then try to model how it changes overtime.
We have come up with mathematical models but few physical models. Mathematical models don't predict anything if you can't physically picture or model how the mathematical model works. For their mathematical models of inflation to have any credence they must be able to explain why we have gravity. Unless, you can provide some evidence saying otherwise, I don't think that has been done yet.
Science is not broken but, I was watching a video by Sean Caroll and in the video he stated it is impossible to get a paper accepted on quantum gravity accepted. Quantum gravity (which will provide an underlying structure to the higgs field and matter) will give us a physical model we picture explaining how gravity works.
Science is never broken but scientists can be very close minded at times and really slow up progress.
Why don't they want to even discuss and look for this underlying order by considering quantum gravity?