To use a simple example, tablebases show that KQ vs. K is won in at most ten moves. But chess books going back many decades, well before tablebases, say the same thing. How was this calculated?
Nothing was calculated. They arrived at their results by trial and error.
Some guy would start with a seemingly disadvantageous position and tried to find the shortest mate. His result remained valid until the next guy found a more disadvantageous position or a quicker mate.
A long time later, engines became powerful enough to calculate simple endgames like K+Q v K simply by exhausting all possibilities, but by that time technology was also advanced enough to create the first tablebases.