You don't have to wait for the flash to get hit. However, the flash occurs so astonishingly close to getting hit that no biological system is going to be able to distinguish them.
The flash is an effect caused by the flow of electrons, heating the air. If there are no electrons flowing, there's nothing heating the air, but also no electrical "hit." Technically the electrons are flowing through you before the flash occurs, but for all intents and purposes, it's instant. Technically it takes the lightning a few millionths of a second to heat up the air to 50,000F, so if you have a system that is operating in the millions of samples per seconds range, you could detect the lag between the flow of electricity and the generation of heat. At any slower speed, the flash is an indication that the current has begun flowing very fast in that particular region of space.
As for why it doesn't appear at the same time, that's a fundamental reality of electricity. While we sometimes think about electrical circuits as just wires, voltage sources, and resistors, there are also inductive and capacitive elements. When working with really fast signals like a lightning flash, these play a part. It's possible to transfer a large amount of charge from one section of the air to another without a path to ground, because the capacitance of the air lets it store a charge. For a simplified handling of this, one could look at transmission lines, which are similar but don't have the complication of dealing with ionizing gases (or at least you really hope your transmission line doesn't have ionizing gases. It's typically a bad day for you when that happens!). These can be looked at to understand how electricity which "travels at the speed of light" can result in slower propagation of the effects that we are observing.
Of course, once a path to ground is "found," the resulting circuit lights up into a lightning flash extremely quickly. It's not instantaneous, but dang is it fast. Only the exploratory phase is slow, as we see in some of my favorite lightning videos. Here's one which shows a bunch of branching feelers, which precede the strike, and here's one which shows a nice leader, which actually forms the lightning strike.
Also, potentially of interest is the Marx generator, which is a high voltage generator built on similar concepts of ionizing gasses. This naturally has the advantage of being implemented with bulk components (resistors and capacitors) so that you can see what the structure looks like, and it also strikes twice in the same place (especially if that "same place" is Mehdi "Electroboom" Sadaghdar's fingers)!