What are the possible part of speech combinations for compound nouns?

I am currently working through allowable part of speech combinations for the first two words of an English sentence. It seems troubling to me to allow the first two words of a sentence to both be nouns, but that may well be valid. One such circumstance is with compound nouns where it is rendered as two separate words (I am neglecting hyphenated and one-word versions here).

If I were to have the following sentence:

Tea time is at 3:00 every afternoon.

I would naturally think of time as a noun of course, but I might describe tea as an adjective in this case.

So which combinations of parts of speech can a compound noun take and how would one distinguish which is the correct labeling for the compound noun?