About AliMcJ Expertise I can answer all sorts of questions about grammar and syntax, due to having fielded thousands of questions as a classroom teacher and having had to come up with on the spot answers. I love English.
Question When writing, should "a" or "an" be used before a noun that begins with a consenant but sounds like a vowel. For example, should I write, "He was a NFL quarterback" or "He was an NFL quarterback"?
Answer You have hit on the exact reason for a/an choice -- the pronunciation. The "n" just closes off the "a" sound before another sound with mouth open (vowel).
For this reason, we also say "a university:" the "u" is a vowel, but the sound it makes is not; "an unusual day" has the open vowel sound, and so requires "an" for "closure."
a National Football League quarterback
and
an NFL quarterback are your correct choices.
