Using the indefinite article before "rain"
Rain may be countable or uncountable:
1988 R. Rendell Veiled One (1989) xiv. 188 Rain was streaming down the window, making the glass opaque.
2006 Africa News (Nexis) 27 Mar. The current Inter-Tropical Convergence Zone (ITCZ) south of the Equator is likely to bring about more good rains over the country during the next three weeks.
"Rain", in common with most weakly uncountable nouns, if preceded by an adjective - a + adjective + rain - then the adjective has a partitive effect:
A noun, when used uncountably, describes a set of homogeneous items. However, that set has subsets (i.e. types), e.g. "A knowledge of French"; "A warm rain fell"; "A deep sorrow affected him", etc.
The use of "a/an" is licensed in a/an's meaning of "one example of"; "a type of".
The OED puts this as
I. Indicating indefiniteness.
- Used in an indefinite noun phrase referring to something not specifically identified (and, frequently, mentioned for the first time) but treated as one of a class: one, some, any (the oneness, or indefiniteness, being implied rather than asserted).
a. Before a noun denoting an individual object or notion, or denoting an individualized substance, quality, or state, and before a collective noun.
1847 H. W. Longfellow Evangeline i. i. 59 A celestial brightness—a more ethereal beauty.
This question is based on an erroneous assumption - that rain is never countable.
In many tropical countries the produce of the land in grain or roots, during the whole year, depends upon one rain in the spring. (Familiar Letters on Chemistry; Liebig, Justus, Freiherr von; 1843)
In the drought-disaster areas, everyone knew that one rain does not break a drought, but farmers and townsfolk alike drew a deep, fresh breath and hoped. (Rain; TIME, 1953)
But since February, most of the county has seen only two rains , each registering less than half an inch. (FOCUS ON DROUGHT IN THE HEARTLAND; Jim Yardley; Atlanta Journal Constitution, 1996)
Right now, two rains into the rainy season, there's enough water and food for the group to travel together, but just barely. (Almost Human; Mary Roach; National Geographic, April 2008)
Since then, there have been three rains, followed instantly by prayers of thanks. But now the dry season begins. (Echoes of the Great Dust Bowl; Hugh, Sidey; TIME, 1996)
Though the non-count use may be the more common by far, the count use of rain seems well established, even without a modifier. In the right context, it's perfectly natural.
The meaning of rain in the above is simply a single instance of rainfall. From the American Heritage Dictionary,
rain
n.
1.
a. Water condensed from atmospheric vapor and falling in drops.
b. A fall of such water; a rainstorm.