Thee cause was probably a combination of speculation, leverage, overbuilding, and so on.

No one really knows the exact trigger, but a popular opinion seems to be that the Smoot–Hawley Tariff Act made it worse -although even that is debated.

The stock market crash lead to margin calls and the sudden evaporation of millions of dollars of wealth and that probably triggered a cascade effect, as business obligations could not be met due to the sudden loss of wealth.

You're conflating the October 1929 stock market crash with the Great Depression. They happened around the same time and they're related but they're not the same thing. The 1987 and 2001 stock market crashes didn't cause decade-long depressions, and the 1987 crash was a larger drop than 1929.

One-day crashes make headlines but aren't that damaging to the underlying economy unless it's already very brittle.