Is soon a common noun or proper noun?

The Word 'soon' is not a noun.
The Word 'soon' (sooner, soonest) is an adverb, a Word used to modify a verb, an adjective or another adverb.

Example functions:
We will open soon. (modifies the verb 'will open')
All of the soon obsolete models are on sale. (modifies the adjective 'obsolete')
We'll be there soon enough. (modifies the adverb 'enough')