xkcd

And we gained a pretty damn good idea during World War 2 and the Cold War when we were trying to map parts of the ocean floor for submarine warfare purposes, and discovered the mid ocean fault points. Especially the true extent of the ~~Mariana Trench,~~ Mid-Atlantic Ridge which is spang in the middle of the Atlantic between the jigsaw puzzle coastlines of Africa and South America.

Needless to say we weren't to keen to blab to our enemies just how much we knew about the seafloor, and neither were they. What with submarine warfare being a Big Deal in the Cold War, and all.

Edit to add some additional detail now that I'm not pecking on my phone: Alfred Wegener proposed his almost-modern theory of continental drift in 1912, as well as the hypothesis of Pangea, the prehistoric supercontinent from the time when all the current major landmasses were together. You're right that there was not a solid explanation for the mechanism by which this proposed action ought to occur. But even by the 1940s scientists were proposing that continental drift happened by way of the continents floating on convection currents of magma underneath and predicted there would be expansion joints in between them in the middle of the oceans.