How I achieved this creative design with After Effects in 5 minutes

Here's a step-by-step guide to creating the smooth circle transition effect you described in Adobe After Effects:
Step 1: Create a New Composition
1. Open After Effects.
2. Create a new composition by navigating to Composition - New Composition or pressing Ctrl+N (Windows) or Cmd+N (Mac).
3. Set your composition settings (e.g., 1920x1080 resolution, 30 fps, and a suitable duration like 5-10 seconds).
Step 2: Create a Circle
1. Select the Ellipse Tool from the toolbar (or press Q).
2. Hold down the Shift key and draw a circle that covers the work area.
3. Ensure the circle's anchor point is centered. Use Ctrl+Alt+Home (Windows) or Cmd+Option+Home (Mac) to center the anchor point and Ctrl+Home or Cmd+Home to center the circle in the composition.
Step 3: Animate the Scale Property
1. With the circle layer selected, press S to open the Scale property.
2. Create the first keyframe at frame 0 with the scale set to 100%.
3. Move the playhead forward by one frame (use the Page Down key or manually drag the playhead).
4. Create a second keyframe with the scale set to 0%.
5. Play the animation by pressing the spacebar.
Step 4: Apply Easy Ease
1. Select both keyframes by clicking and dragging over them.
2. Press F9 or right-click the keyframes, go to Keyframe Assistant - Easy Ease.
Step 5: Adjust the Graph Editor
1. Open the Graph Editor by clicking its icon in the Timeline panel.
2. Adjust the graph handles to create a curve where the animation starts slowly and ends quickly. Drag the left handle higher and the right handle closer to the base.
Step 6: Duplicate the Circle
1. Select the circle layer and press Ctrl+D (Windows) or Cmd+D (Mac) to duplicate it.
2. Repeat as many times as needed (e.g., create three circles).
Step 7: Offset Start Times
1. Arrange the layers in the timeline by dragging their start points so each begins slightly after the previous one.
2. Ensure the intervals are small to maintain a smooth transition.
Step 8: Add Colors
1. Select each circle layer and apply different colors via the Fill property in the Shape Layer settings or the Toolbar.
Step 9: Final Adjustments
1. Preview the animation and ensure the intervals between circles create the desired effect.
2. Adjust timing and colors as needed.
Result
Now you have a smooth circle transition effect!