Here is a short answer, from
here
A common complaint of Creationists and the Intelligent Designers is that the mutation rate for advantageous mutations is so small that even the more than 3 billion years that life has been present on the earth is not enough to allow for Darwinian selection of advantageous mutations. [p79] Creationists and the Intelligent Designers repeatedly claim that the production of beneficial variants by single nucleotide mutations (STMs) is too rare and too slow to allow for evolution. This ignores the fact that much evolution is not the result of this type of rare genetic change. DNA composed of repetitious sequences in the form of short tandem repeats (STRs) mutate a million to 10 millions times faster than STMs and play an important role in gene regulation and evolution. In addition to this mechanism, reusing or exchanging pieces of DNA that have already proven themselves in other situations accomplishes most evolution. These processes for rapid evolution include:
- Endosymbiosis
- Whole genome duplication (polyploidy)
- Chromosomal rearrangements
- Gene duplication
- Hybridization
- Gene displacement
- Horizontal gene transfer
- Jumping genes
- Sexual recombination
- Retrotransposons (Alu sequences)
- Exon shuffling and domain exchange
- Repetitious DNA and repitious peptides
These processes allow whole genomes, whole chromosomes, parts of chromosomes, whole organelles (chloroplasts and mitochondria), whole genes, specific combinations of genes, whole gene domains, and parts of gene domains to be put to new uses over and over again. This reuse of what already works allows for the rapid acceleration of evolution and speciation and allows for a rapid response to environmental change and geographical isolation. As a result there is plenty of time for evolution to occur. [p92]
The basic answer is this: This is one of the first questions that Biologists asked about this theory. It has been tested and prodded and poked at and challenged by some of the world's best minds for over a century, and they were reluctantly convinced that the answer is yes around 100 years ago, when we realized that the earth is over 4 billions years old.