Our date system is like the Fahrenheit system; it works well when thinking like a human.
in Fahrenheit, you just think of it in terms of 50 being the middle, "not cold and not hot". Then you understand 80 is high warm, closing in on hot, etc.
Similarly for our date system, we lead with names and important information rather than numbers. We're not feeding a number into a machine, we're speaking to humans.
Consider any other Label. You don't say "25th Apartment", you say "Apartment 25", "Unit 25", "P.O. Box 25"
Here we are on March 25. The year comes last because it's least important.