The first thing you'll need to know to PB on this run is to jump. Your horizontal velocity is higher if you jump than if you don't jump, it is still uncertain whether or not your airborne speed is higher than your grounded speed and if jumps simply give you a horizontal speed boost (this would clarify if small jumps are faster than higher jumps), but one thing is certain, jumping is faster than walking (you can test this using the destroyable wall next to the first spirit).

The next thing that you'll need to know is to move as soon as you're able to. This will ensure that the first spirit is at its closest point to you during your run.

The last thing that you probably need to know is that when you jump there is downward vertical acceleration which implies that if you want to get the first spirit and fall onto the "pit" as soon as possible you'll want to jump early to give you a non-zero vertical velocity when passing the same height as the floor (big words for you'll hit the floor quicker because you won't need to accelerate as much).