Starting off, I broke up the elements to be animated. The letter 'G' of the google logo consists of four colors: blue, red, yellow and green all mixed in one letter, and at the same time, the logo is circular except for the dash in the letter 'G'. So I made three circles and one half circle.
Jumping into After Effects, I imported the artwork and converted the layers to shape layers to work with them in after effects.
The main technique I used to animate the logo here is the trim paths shape modifier in After Effects, with each letter parented to a null to zero out their main properties (DUIK lets you do this easily, download DUIK from here). Now that all the shapes' properties are zeroed out, you can start animating with "zero" worries.