I’m considering putting up a poll on the very first music you were aware of.
Help me build a list of options.
Parent’s singing
Other family member singing
Somebody in the family playing:
– piano
– guitar
– harmonica
– other instrument(s)
Radio
TV
Juke box
Church
Family record player (LP, tape, CD, computer)
Street performer
What am I leaving out that would apply in your case?
[typical precocious Doper] I was writing my own songs before I was two.[tpD] 
Righteous! Top of the list. Item #2: angels.
Ice cream truck
TV theme songs (as opposed to music on a TV show)
Church bells
Toys (toy piano, xylophone, jack-in-the-box, etc.)
Music box
Cartoons (especially classical)
Elevator music (elevators, stores, malls, etc.)
Cell phone ring tones
Kids’ games, taunting, etc. (e.g. skipping rope)
Nursery rhymes
Excellent, panache45!
Parents singing
Records
Radio
TV
Other than nursery rhyme type music (This Old Man, The Framer in the Dell, etc) my first childhood exposure to music was classical and/or opera as my mother has been a long-time opera nut.
Mom loved to sing. When she was in high school, she was in a group with 2 other girls doing Andrews Sisters songs. They were even on the local radio once or twice. So I never really noticed music, it was always there.
“In early memory, mission music was ringing round my nursery door” --Paul Simon
Music is pretty ubiquitous in most people’s lives these days, so, given the almost universal prevalence of childhood amnesia, I doubt whether anyone truly remembers their “first exposure”, not if you are counting things like TV themes and the radio. I do remember some old 78rpm records my parents had, that I used to dance about and sing to. I am not quite sure how old I was, maybe 3 or 4 or so. For some reason I would often hold an orange in each hand as I danced. One of them was called "Cigareets [sic] and Whusky and Wild, Wild Women" . 
(I am not sure if the version at that Youtube link is the same performer, but it could be.) Another one was some sort of Hawaiian ukelele instrumental, called K??? Hotel.
There was a piano in our house, but nobody in my immediate family could play it.
Dad played guitar and sang; I was in my late 20’s before I realized that “Me and Bobby McGee” was not written by my dad about my mom, whose maiden name that was. 
Mom sang around the house.
Friends of my folks came with guitars and played together, banjos too.
We had a record player. I remember Peter, Paul and Mary.
My favorite toy was a kid’s record player. It had pre-formed, pastel-colored plastic disks and made the same kind of plinking music that little music boxes do. Claire d’Lune for the win 
And of course Sesame Street.
OOOOOH…Jukebox! I kid you not. My mom would go to coffee with a friend, and the coffee shop had a jukebox. I always thought it so very wrong that ‘Please, Mr. Please <Don’t play B-17>’ was not, in fact, selection B-17. 
First song I remember is hearing You Got a Friend in 1971 in an apartment in Atlanta.
I think the first music I was aware of was the Mull’s Singing Convention on Granma’s TV. I learned to sing gospel songs out the ass. 1955.
Are we talking about “first being conscious there was music” or “first becoming interested in music”? The first one falls in the realm of “can’t remember”, an option the OP did not include. Music has been part of my life since forever, between church, TV, radio, movies, local festivals…
My mother singing lullabys.
She also played the guitar.
But what really made the biggest impression was my grandmother’s record player. An old tube model, which took time to warm up. You could look through the grille and see the warm glowing orange light of the tubes. And it had a wonderful warm electronic smell.
The song I remember as my “first” song? Nat King Cole’s “Nature Boy.”
Birdsong?
Deep in the most microscopic structures of the Universe, beyond atoms and protons and electrons, beyond photons and quarks and gravitons, beyond the vague abstract complex probability wave functions of which all larger structures are just superpositions, is the ultimate fundamental Music of the Universe, the sweet vibes of Ilúvatar and the Ainur.
But the Universe contains Pain and Suffering and Evil as well! A bit of discordant Music thrown in by a Maia or two gave us that.
The OP said
and I will make no further effort to clarify that.
These would be pre-kindergarten:
Mom singing nonsense songs to me:
“It was an itsy bitsy teeny weeny yellow polka dot bikini”… “Hennery the Eighth I Am”… stuff like that. Yeah, I know it’s “Henry”, but Mom always sang “Hennery”.
Records playing and both parents singing along with them.
Radio, quarters in the jukebox at the pizza parlour.
We didn’t have a TV til I was in grade school, so no TV themes.