It doesn't matter. That's the beauty.
You can fire the particles such that there is a large time interval between them and we still obtain the interference pattern.
Note that The particle always hits the screen at a definite location. As time goes on, more and more particles hit the screen and the pattern formed is alternating light and dark bands.
What's more surprising is that when you observe the particles and can definitely say which slit the particles went through the interfence pattern reduces to two classical peaks behind the holes.
This is one of the best experiment to understand the difference between classical and quantum mechanics.