根据 facebook policy 社交插件4点状态：

不要模糊或覆盖社交插件的元素。

你不能直接改变图像，因为它是由Facebook提供的。

I have created a custom Facebook like button.

How do make it that when I click the button, it will trigger the like button provided by Facebook like the one below?

According to facebook policy on Social Plugins point 4 states:

"Don’t obscure or cover elements of social plugins."

You can't change the image directly because it's provided by Facebook.