There is a reason it is called the Theory of Evolution instead of the Evolutionary Principle. It is a model that fits the facts and is revised, as necessary, as more data becomes available. An irony that seems to be lost on most YEC types is that theories evolve until they are proven correct or incorrect.
Still timeliness is a relative term based on generations. That’s why most historic models have primarily been Monera due to the logarithmic reproduction. Only recently have new models been chosen (GGG posted an article last month about that). Evolution in the larger scale is still unobservable directly in living models due to the human life span - go figure, eh? Ultimately it’s a theory in progress and is the best foundation that we have to build from even if we must occasionally tear down parts and rebuild it.
The fossil record is a testament to evolution. We see vast gulfs of time filled with unbelievable animals for long ages of the Earth, mass extinctions, and the rise and domination of new forms. We see marsupial mammals giving way to placental mammals everywhere on the planet (except opossums and Australia), and then we see it happening before our eyes in Australia with the introduction of placental mammals that now dominate the ecosystem.
Mutation processes are most certainly probabilistic. One cannot induce the exact same mutation consistently as if it were some programmed response. They take place more often in some locations that others because some sequences are chemically or positionally more prone to mutation.
Do you think random means ‘beyond God's control’? The dice fall in the lap, but every result is from the Lord.
Punctuated Equilibrium (PE) was never suggested as an explanation for why mutation is probabilistic not random. Did you just need a segue? PE didn't extensively modify the theory of evolution through natural selection of genetic variation, it explained why we would see what we see in the fossil record and modified the idea of ‘gradualism’.
Gradualism is the idea that if you see fossils of a ‘flying squirrel’ that seems descended from a less aerodynamic squirrel fossil species from two million years before, a squirrel from one million years before in that lineage should be ‘half-way’ towards being a ‘flying squirrel’.
PE and most studies on how speciation actually happens or happened have shown why that is an incorrect assumption; but neither has changed the theory of evolution through natural selection of genetic variation.
“time needed”??? Evolutionary theory doesn't dictate how much time has passed, and is not at all dependent upon how much time has or will pass. You need to look at Astronomy and Geology for that.
However once again we get back to my point. CONSISTENCY. Evolutionary theory, Astronomy, Geology, plate tech-tonics, radiometric dating, human history, archeology; all can be used to construct a CONSISTENT timeline; wherein an insistence upon a young Earth is INCONSISTENT with what we know about universal principles of physics, chemistry, and biology.