Start animations simultaneously but have one be delayed.

I have several groups of objects, and they all have a similar (but individual) animation. They all float up and down forever, and the animation curve looks like a sine curve (no pauses during movement).

My problem is that I want one group of objects to have the animation be played slightly later than the other. And I want to know whether I can do this without using scripts that wait some time, then somehow turn on the animation of one of the object groups.

I don't really know how to explain this, so please ask questions if you're not sure what I mean, and I can elaborate.

P.S. The animations are native Unity animations and use the objects' Transform.position property.

 

Here's a little more explanation I thought of.

The red square represents one object group, the green square represents another.
I need to somehow make the green group do the animation slightly after the red one starts, but without having to create any fancy code that checks lots of animation stuff and alters it. Just because this is a very simple animation that is just supposed to play on background objects.

EDIT: I can think of at least 3 ways of doing it, but each one is way over the top on code and Animator management, for what it needs to do.

 

Tried using Cycle Offset, and it seems to be working fine for now.