Why you should know: The ‘a’ vs ‘an’ conundrum is not about what letter actually begins the word, but instead about how the sound of the word starts.
For example, the ‘h’ in ‘hour’ is silent, so you would say ‘an hour’ and not ‘a hour’. A trickier example is Ukraine: because the ‘U’ is pronounced as ‘You’, and in this case the ‘y’ is a consonant, you would say “a Ukraine” and not “an Ukraine”.
Tip: when in doubt, sound it out(loud).
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This is also true for initialisms, which are acronyms in which each letter is pronounced individually.
“A NASA project” would not become “an NASA project” because nobody pronounces each individual letter of NASA, they just say it as one word.
“An FBI agent” would always be correct, and “a FBI agent” would always be incorrect, because FBI is never pronounced as a word, and each letter is pronounced individually.
NASA vs NSA makes this more apparent too. For example:
A NASA investigationvs
An NSA investigationWait, you mean people don’t call the FBI the fuhbby!?
They will now!
You make a valid point. One initialism/acronym I can think of that can go both ways is SQL (Standard Query Language). You can either pronounce it as Sequel (thus “a sequel query”), or as individual letters (“an S.Q.L. query”).