Separation of Church and State

Many people will be shocked to learn that this term does not appear in the U.S. Constitution


The often looked to spot for this "separation" is the first amendment, specifically the first part:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof;

Hmm... So when some one files a suit complaining about the "government endorsing religion" where do we turn to decide the case?

The Supreme Court (this case isn't at that level, and I don't know about federal courts, but lets pretend it makes it to the Supremes) is limited to interpreting the constitution, so can anyone tell me how the Justices could do anything but throw a case like this out?

Congress has made no law. Therefore the first amendment is not broken. Therefore the Supreme Court must throw the case out.

Or am I missing something?