OpenToonz' particles are only 2D, so you need to fake the appearance of depth.
Here's my method:
Connect a white circle to the Particles' Texture1 input, you can use anything you like but this is good enough.
Create a RadialGradient, set Color 1 to Black and Color 2 to white, make sure both have an alpha of 255.
Set the RadialGradient's Outer Size large enough to fill the entire canvas.
It should look like this:
Connect the RadialGradient to the Particles' Control1 input, this will be used to control the direction of gravity for the particles.
Width and Height - Set these so that they fill the entire canvas.
Starting Frame - You can set this to a negative value so the animation starts with a lot of particles already created.
Speed - Set this to 0, we don't want any initial movement when each particle is created.
Size - Set the min and max to a small value, this will make the particles initially appear distant.
Top Layer - Set this to Older, this ensures that the particles that appear closer to the camera are drawn in front of the more distant particles.
Gravity - Set this to a positive value e.g. 15, the higher this is, the greater the acceleration.
Gravity Control Image - Set this to 1, this will use the RadialGradient we set up earlier.
The particles should move outwards towards the edges of the screen.
Fade-in Frames - Set this to your liking.
Size Intensity - Set the min and max to a fairly small value e.g. 1, this will cause the particles to grow in size, creating the illusion that they are approaching the camera.
That's it for the Particles' settings, you can add a RadialBlur effect to help emphasize motion.
This is my final result, it isn't perfect but that can be fixed by tweaking the settings more: