Historically (I think) Cha-Cha developed from Mambo, which breaks on the 2 beat. Musically (an instructor pointed out) there is a difference between starting a movement on the downbeat (1) and the upbeat (2). That's the reason why Mambo and Salsa look different even though many of the steps are the same. Breaking on the downbeat makes it look more "laid back." Breaking on the upbeat makes it look "sharper" (more "upbeat").
Technically, the rhythm (slows and quicks) is the same but the timing (which beat of the music a movement starts on) is different. The instructor I mentioned demonstrated this by dancing a simple Waltz box, but stepping forward on the 2 beat instead of the 1 beat. And he was right; it looked different.
You can start with 1. It's called a prepatory step. Rumba is the same way, where in international style you do a prep step on 4-1, and start on beat 2. American style rumba starts on beat 1. Cha cha is the same in both.
The count doesn't start with a 2. That's the point that a local instructor (NOT the instructor I mentioned in a separate post, who concentrated on the difference [and the relationship] between rhythm and timing) makes. This instructor's view is summed up in the statement that the dance is the Cha-Cha, not (as you often hear) the "Cha-Cha-Cha."
Again, it has to do with the music. A measure starts (obviously) with the "1" beat, and in the case of the basic movement the dancers take a side step on this beat. The measure ends with a chasse (4-&). The next step is a side step, taken on the 1 beat of the next measure. Her view is that thinking of the combination (chasse followed by side step) as "cha-cha-cha" is wrong, and leads to sloppy dancing.
In the International technique, the dance is called the Cha Cha Cha (three syllables).
The Laird Technique of Latin Dancing (2003) states that the first two steps of the Cha Cha Cha Chasse are danced on 4 &, while the last step of the Chasse coincides with beat 1 of the next bar of music.
Further, the dance is supposed to be started on beat 1.
The origin of Cha Cha, is Guajira ( breaks on "1" ) and also danced in mambo,old school, called triple Mambo .Guajira is also a dance in its own right .
Latin music ( Son Rhythms ) are quite specific in their intent, and Guajiras, to many, may sound like Cha Cha,to which one may dance Cha Cha.. but.. the Cha Cha composition only has one syncop. action which " joins " 2 bars together, if you will as in 4and 1.
The syncop. in Guajira, is included in the same bar.. 1,2,3and4. There is frequently a 2nd syncop. , that is not as dominant on the 2nd bar .
The commencement of Cha Cha, differs between the Amer. style and Intern. Amer. style commences its break, back, as opposed to the Intern. styles Fwd break. Both are " prepped " on 1 .
Chas back break beginning, is using the same format, as Mambo and Bolero ,in the Amer.style dances.
If you want to hear what a classic Guajira sounds like, check out " Guantanamera ".. there are numerous recordings ( believed to be the most recorded song in the genre ).