I was wondering if one could start ear training too early in learning music?
It's never too early to start ear training.
Pre-school children start training their ears when they listen to their nursery teacher singing nursery songs, and they then copy her singing Twinkle Twinkle (or whatever they sing these days). Those who are brought up in musical families - like little Wolfie (Mozart) - start their training much earlier, from before they were born, when their mother sings or plays music.
Therefore, start with Twinkle, Twinkle. If you play a 3-note major chord on the piano (say, C-E-G), can you sing/whistle/hum the first note of Twinkle in the right key, without fumbling around?
If you can, try it with the first note of The Star-Spangled Banner (assuming you are American, otherwise use your own country's National Anthem).
Then, can you tell which notes in the major scale the notes of the music fall on? (Next, learn about basic intervals - can you tell what the intervals are between the first two notes of the above? If you can 'hear' where the notes fall on the scale, and you know the intervals between the notes in the scale, you'll know what the intervals are between them.)
And clap along with the beats in the song (while singing, or listening) - where are the strong beats? How many beats in each measure? Can you beat time to the music depending on whether it is 2-, 3- or 4- time? (Duple, triple, quadruple)
Do that with every simple tune you know of, whether it's a folk song, a pop song, a hymn. That's how you can start doing basic ear training. Lots of careful listening, lots of singing.......(doesn't matter how "bad" your voice is - you can still learn to sing in tune!)
You should learn to identify straightforward intervals (major 2nds, major & minor 3rds, Perfect 4ths & 5ths, major 6ths) - and sing
them - first before you go on to any chord identification. Too many students attempt to jump in at the deep end and try to 'hear' diminished, augmented chords etc before they can even identify simple intervals.