Alfred Wegener developed his theory of continental drift in the early 20th century. His theory wasn't well accepted at that time. Geologists of that time had their own not quite scientific ideas regarding orogeny (mountain-building) and continental boundaries. Geologists of that time, along with biologists of that time, were also battling religion. This outsider (Wegener) with ideas that continents somehow plow their way through oceanic crust was not deemed plausible. In addition, his ideas were also deemed a bit too close to the mostly religious catastrophism geologists had been fighting for decades.
Wegener was hardly the first to see that the continents fit together like pieces of a jigsaw puzzle. What Wegener added was fossil evidence that at some time in the past those jigsaw puzzle pieces must have fit together. What his theory did not have was a mechanism. He posited that continents somehow plow their way through or over oceanic crust. He had no mechanism.
Plate tectonics, while perhaps motivated by Wegener's continental drift, is a theory distinct from continental drift. In particular, plate tectonics does have mechanisms. Before I get to those, I'll address your key concern.
However, according to the Plate tectonics, there is much space (let's name it A) on the right-hand-side of South America and much space (let's name it B) on the left-hand-side of Africa.
If these 2 plates were near to each other so that the two lands meet, where did the space A and B go? I think there are only 2 possibilities:
- A was over B,
- B was over A.
You are missing a third possibility, which is that the spaces you are calling A and B didn't always exist. This is exactly what plate tectonic theory says has happened. New oceanic crust is created by volcanism at the mid-ocean ridge. This newly formed oceanic crust is one of the key mechanisms by which continents move. Another key mechanism is subduction. Oceanic crust sinks into the mantle at subduction zones.
These two mechanisms mean that most oceanic crust is fairly young, less than 200 million years old. The oldest oceanic crust is probably the Herodotus Basin in the Mediterranean Sea, estimated to be about 340 million years old. In many ways, it's best to view the Mediterranean Sea as a remnant of the old Tethys Ocean rather than as an arm of the Atlantic Ocean.
The space we currently see between South America and Africa did not exist when the supercontinent Pangaea existed. Rift valleys formed that started to split the supercontinent into pieces. These rift valleys eventually became the sites of new oceanic ridges, and the space between the split-apart continents became new ocean such as the Atlantic Ocean.