A lot of people are like "we got to the moon in the 1960s, where's the progress we should have had since then?" but I see the 1960s as the bizarre exception rather than the thing that should be used to set the rule. There was no way the space age was going to happen then, in an era where you're almost sitting there counting each bit of RAM you can afford to send into space. The true Space Age is just dawning now, and it's still early in the dawn; we still have to have massive international cooperation to put a single space station up, we can't do something as basic as refuel in orbit, we just barely started having people in space for commercial rather than governmental reasons... it's just the beginning.
The apollo program drove the need for more computational power, more memory, better guidance and navigation and control systems, better materials, experiments to better understand many phenomena, etc. And after the apollo program ended, the contractors that developed those technologies on NASA contracts could just commercialize them. And the data from experiments, on materials, aerodynamics, combustion, and so on, that is publicly available has made engineering so much cheaper and easier.
And yet, they got to space. Better computers are not the solution to every problem. And it wasn't a false start. We are already in a space age, we have been for quite a while. It didn't stop at Apollo. We have satellites for the military, TV, weather, various forms of communication, navigation (GPS...), telescopes, space stations, probes and rovers. We do science, commercial and government operations. Starlink is great, but it is just the continuity of all the space communication abilities we developed over the years.
I think computers are not what will enable the "true space age". Sure, they help, and SpaceX, if successful with their Starship will certainly be a big advance, but I think that we are missing a key ingredient to reach the "true space age" and it is nuclear power. Starship maybe could get us a settlement on Mars with hundreds if not thousands of launches and refueling missions. Project Orion was to launch an entire colony in one go, return trip included. Even Saturn was considered feasible. Project Orion is mad, but it goes to show how limiting chemical rockets are compared to nuclear.
And it is something we probably could have done already, without modern computers and 3D printing, if we wanted to. It is maybe a good thing that we didn't though. Spreading radioactive material in the atmosphere and mass producing thermonuclear bombs is kind of scary.