Of course it is, and you are simply working your own mind overtime to deny what is obvious:
Evolution (whether "micro-" or "macro-") consists of two main confirmed observations = facts:
The only issue here is how many iterations of this process are we talking about, and when, exactly, do we define a new "species"?
By any definition the historical record on, for examples, dogs and cats, shows that just a few thousand generations can produce amazing new breeds, but do not produce new "species."
But if you could isolate one species for millions of generations, selecting each time for some special characteristic (i.e., adaption for cold climate), you would easily find that at some point the isolated species will no longer interbreed with other descendants of their common ancestors.
Hence a new "species".
Mudtiger: "Starting from species 1, build the new genome mutation-by-mutation that results in the new species."
The ancient records of "mutation-by-mutation" are readily available through DNA analyses showing where, exactly, are the differences between one species and another.
If you'd like a surprising example, consider the little Hirax and elephants, whose similar DNAs shows them as closer related than anyone had previously suspected.
Mudtiger: "Or to make it easier perhaps, start with a fin and describe the mutations that eventually result in a leg and how all intermediate mutations were beneficial on the way from swimming to walking.
Then you have a mechanism.
Otherwise, it's just an assumption "
Far more than "assumption," when there are many living examples of "intermediate" steps between swimming and walking, when the fossil record shows many more, and when DNA analyses show how closely related are characteristics of one particular species to another.
It is just these kinds of evidence which make evolution not just another scientific hypothesis, but a confirmed theory.
Mudtiger: "I don't think evolutionists can describe such a path/mechanism that would be realistic even in their imagination."
The natural world, including fossil records are chock full of examples of "intermediate steps."
These are exactly reflected in DNA analyses of modern species.
So what, exactly, is your problem?
Similarities in DNA can be used to support modular design as much as support common descent. Since many (most?) lifeforms carry out many of the same basic functions on molecular scale, it makes sense that they would have some DNA in common, whether designed or evolved. Intermediate steps may not be intermediates at all but created species that went extinct. The evidence is the same, it's just how does one interpret the evidence.
"My problem" is that no one has solved the details of the mechanism that explains which mutations occured in changing a fin to a leg (for example) and why each specific mutation imparts greater survivability so as to predominate. Just an assortment of general statements are offered.