The night is still young = It's still early in the evening. (So, there are many things we have time to do - or can still do.) The opposite is: It is very late in the evening. (There isn't much time left to do much because it is too late in the evening now). There are many ways to say that it is late in the evening. "Wow, it's really getting late." < Is probably the most simple way to express this.

What's the opposite of "The night is still young"? It's getting really late. The night is almost over!

The night is almost over or It's almost dawn

The night is almost spent.