My shot: give the button borders (bottom and right) of a darker color than the background, change its size when its clicked (active).

Code:

<button className="mt-4 px-12 py-3 rounded-lg text-white bg-blue-600 border-b-8 border-r-8 border-blue-800 active:border-b-4 active:border-r-4 transition-all duration-100">Click me</button>

Gif: