I talked to someone from Mexico and when I was talking to him about my trip he said in reply:
I asked my Mexican friends what it meant and they said it's like "cool" but they didn't know in what era it was used.
Could anyone tell me?
As a Native mexican, I can tell you from my personal experience that it was more common to use that expression on the 80's/90's than it is nowadays, as it sounds kinda outdated. But it's much older than that.
For example there's the movie "Fíjate qué suave" from 1947, featuring the comedian Manolín, which used "Fíjate qué suave" as his catchphrase even before before the movie.
It was common in the '70s when I came to New Mexico. Still hear us Seasoned Folks using it.
Kind of the same thing as 'Que Sapo' as pronounced in a drawn-out fashion. My father-in-law said as a kid somehow someone had a decorative or toy frog. Instead of having electronics, kids would pitch/toss pinon (nuts) at it and if you got it in its mouth, you were teased that it wasn't 'cause you were skilful, but just lucky. Albeit you got to win the other pinon (a delicacy in NM) that had been thrown! Que Barbaro, Hombres!