When a population encounters a change in environment, it may be the case that, due to natural variation, certain individuals are better able to physically (or mentally) adapt to that environment, so those individuals will do better in the new situation (becoming stronger, or faster, or holding their breath longer, finding clever ways to obtain food, etc.) and so out-compete their fellows, being more successful in the reproductive stakes, and passing their adaptable genetics to the next generation. So over time, the mean fitness of the population for the given trait will increase, and without the selective pressure of the old environment, fitness for the old environment will decrease.
So it is possible to have individual adaptation before the population genome 'catches up'.