It's a little tricky to achieve what you want to do. I attached a sample file that you can try to follow. In the sample file, I have 2 divs, one red and one pink. The red one is supposed to animate first with the pink one not visible, when it reaches a certain time, red div disappears and the pink one starts to appear and animate. Here are the steps:
1. Set up the animation for your first element.
2. Switch to Timeline Advanced mode and add a
timeline event to turn visibility for the second element to hidden with the following steps:
a. Right click on the timeline Event layer and click Add event.
b. Double clicking on the timeline event marker and select CSS for Action, Set styles, pick the element id for the element you want to hide as the receiver (make sure the element has an id in the Properties panel).
c. Click the + sign to add property to change and type visibility for property, and hidden for value.
3. Set up the animation for your second element.
4. Drag the first keyframe of the second element to the point where you want it to initiate animation (animation delay).
5. Add another timeline event to turn visibility for the first element to hidden and the second element to visible by using custom action since you want to change properties on 2 elements. Please look at my test file.
You can also try to import an animated gif in Google Web Designer.
Hope it helps.