TL;DR meme is wrong. It’s not the communication of information but the invention of specific technologies that allowed it

Space tech was well and truly developed decades before the internet was anything more than a curiousity.

Rockets are the primary underpinning tech of space exploration - invented centuries earlier but refined enough in the 1930s and 1940s for the Germans to put them into space en route to blowing shit up.

If you’d said “computers” it might be a better argument: while the first peacetime spaceflights were calculated by humans with pen paper & slide rule / log tables, primitive computers were soon brought in and helped in accelerating progress.

Same with exploration, it wasnt printing press in 1500s that expanded exploration (books had been around for several millenia before 1500AD), but the invention and widespread use of the sextant and accurate clocks allowed more precise navigation