Evolution is put forward as an explanation for the nested hierarchies of life forms. It is almost blindingly obvious that if each new life is an offspring of a previous life but with modifications then they have to be in such a nested hierarchy.
The fact that the model demonstrates a capability of producing the found results is on reason for accepting it's validity.
Another demonstration is the flow of modifications we see through time in the fossil record. The imprinted record of the rocks is also just what the model would suggest we'd find. The fact that as the fossil record has slowly been filled in following the expected pattern is further strengthening.
After the rather detailed development of the nested hierarchy over centuries (starting well before Darwin's time) a powerful amount of support is obtained from the high degree of match between the hierarchy of the forms of life and the same pattern imprinted in the DNA of those life forms.
All that and more gives us an explanation that matches the known facts. When centuries of effort can't come up with another explanation that works as well then we accept the existing model's validity.