There was plenty of evidence from other countries at similar stages of the epidemic. This is not hindsight, the models and data were available from day one (mid-March) in SA, if only the right people were looking at them...
Our government built their model from data out of Wuhan and from our own flu cases that get tracked each year.
There are people here on the forum who now go "oh, look, someone else says the data from a projection was flawed, I was saying this all along!", but in reality no-one knew where the virus was going to go. You make the best decision with the information available, and at the time it was all hell breaking loose in every other country in early March.
In one month, over 11,000 unpublished papers were written, documenting COVID-19 cases. That's a mountain of data to sift through.
Even now, the models are inaccurate because now we know that most stats are out by a factor of ten or more because there are far more asymptomatics than previously thought.