Okay so let me clarify something. There are two different ways to understand the word “evolution” which frequently get mixed up if one is not careful to specify what they mean.
One is:
(1) The process by which evolution occurs (how do organisms change over generations?)
and the other is:
(2) What has happened in the past history of life (what did modern organisms evolve from and how are they related, if at all?)
The first one (1), the process of evolution, is technically defined as “transgenerational changes in the frequency of allele genes in populations”. Evidence for the reality of this process (the fact that this is something that happens, that organisms change over time) is the observation that carriers of different alleles (technical term for different mutant versions of the same gene) can be shown, by observation of wild populations or by observation of laboratory experiments, to change over generations. The frequency really does change.
Evidence for the second one, the past evolutionary history of life (and the common descent of different species), is shown by a combination of the fossil record, and by comparing the DNA sequences of different species of organisms and (among many other things) deriving phylogenetic trees from them, and then by comparing the degree of match of their (technical term incoming) branching topology (basically the order of the branches in an “evolutionary tree”).
So when somebody asks for “evidence for evolution”, it’s hard to know whether they are asking for evidence that evolution is really something that happens (that organisms change over time), or if they are asking for evidence for the past evolutionary history of life (including the common descent of different species)? They usually mean the latter.
Nobody here claims that evidence that evolution is something that happens, is also evidence that all species have a very deep evolutionary past and share common descent. The evidence for common descent and the deep evolutionary history of life is not the same as the evidence that organisms change over time. Even thought the subjects are related, and in some sense tie together into an overarching framework under “evolutionary biology”.