this is an easy job for text animators in Ae: Animating text in After Effects
if you got a references then let's examine it. we have got position from Z space, blur, and opacity.
so create a text layer, make it 3D, add an animator and enable per character 3d in the animator menu while you are at it.
add these 3 properties: position, blur, opacity. set the initial value for all three. if you want overlapping animation you can choose "Ramp Up" under advanced and set randomise order to ON. now keyframe the offset.
here you go: