With most science, there is very rarely (if ever) one piece of firm, unquestionable evidence: more, it's lots of small bits and pieces that just add up to make suspicion a more than justified position.
Firstly, there are gaps of the figurative kind: any honest scientist will admit some aspects are not fully understood. This isn't a contradiction: it's entirely possible if the world were round too.
There are also gaps of a literal kind: nature is not so ugly as people suppose. There are patterns to be expected everywhere: in the RE model, approximately spherical objects form commonly in space, elliptical orbits too being common. And yet space is so uneven in composition: there's a very powerful thread in the SaAS section which shows the Solar System to scale, and the sheer diminutive nature of every solid body is really quite shocking given how much space they had to form in, and how much matter must have been involved to begin with.
There are undeniable conveniences all the way from the start of the RE model (such as the rapid expansion), which again may be explained by things such as the anthropic principle, and further gaps-to-be-filled. Another example would be how we are in the prime time, cosmically speaking, to observe the universe: theoretically the window of opportunity would be far greater in a FE model.
There are bits and pieces in every field, from the importance of mass to both space, time, and a hypothesized Higgs field, to the behavior and importance of light.
None of these (or the other queries) alone are nearly enough to justify toppling a paradigm. It is the fact that they are all held to be true that makes questioning a very valid pursuit. There may be answers, certainly: there can be answers for many things. What matters is how likely it is for all those answers to simultaneously be true.