Q:

Missing a determiner before countable noun - Sign

At the following page of Cambridge dictionary is the sentence:

There was no sign of life in the building. 

Why is this sentence without a determiner before sign since the word is countable?
This is the sentence that I would make: 

There was a no sign of life in the building.

I guess it has something to do with the word no.

A:

We need to remember what articles are for. "A" is used to speak about something that exists, and that we are mentioning for the first time and/or it is one of many of such entities. "The" is used to speak of something that exists, and that we have already mentioned previously.
However, if there is no sign of life somewhere, there is not an entity to speak of. So "no" provides some pretty specific information—that something is absent; so it's a determiner of its own.
A similar phrase would be

There is no reason to believe that our information is incorrect.
There is no way to help him.

(If there were one, we'd say, "I know a way to help him"—one of many possible ways.)

