What is the minimum time taken by a species to evolve? Let the evolution not be completely advantageous to the species, but still, even a little evolution which can be seen or proved should be okay.
You can prove evolution by analyzing the genome after only a couple of generations.
Evolution is a process, not an event, and every new specimen will have different DNA than his predecessors. Some of the changes give it an advantage, others a disadvantage, or no changes occur.
You will always need a point of origin for your analysis, so a specimen that came a couple of generations before the current. Only this way you can detect changes and analyze their impact on the fitness.
In some cases you might even be able to tell when a specimen has lived according to historic extinction events that greatly influenced the fitness function.