A lot of people are offering explanations, but I think I'm going to give one too.

Think of recoil in a gun. If you don't have a mental image of it, watch a few youtube videos of people firing handguns. Look for videos of big, high-recoil handguns, like the Desert Eagle or the Magnum (or the Super Ruger Redhawk according to chat-GPT).

You need to get a good look at handguns pushed backwards as they are fired.

Now think about this: those bullets aren't pushing against an atmosphere. They are pushing only against the inside of a gun.

But when this tiny, tiny bullet pushes super-fast against the gun, using the gun to accelerate to incredibly high speeds very quickly... it pushes the gun really hard in the other direction.

Get that mental image into your head. Small object can push large object with a lot of force by kicking off of large object with insane speed.

Now: Take away the person holding the gun. Take away the planet. Take away the atmosphere. Put that gun in space and pull the trigger again. (Just make sure to use a gun that has modern ammunition that doesn't require oxygen to fire).

What happens to all that recoil? What does the recoil do to the gun now? The bullet still goes flying out of the chamber. Still does this by pushing against the gun.

Hopefully it should now be easy to imagine that the gun will start moving.

Rocket fuel is basically a tank full of bullets.

The main function of rocket fuel is "heavy stuff that is shoved out of the spaceship to make it move."

The reason we use highly explosive fuel is because "shoving heavy stuff away from you at the speed of a bullet" is going to move you more than "shoving heavy stuff away from you at normal speed."

Does this make any sense?

Every action has an equal and opposite reaction

Think of it like this, imagine you are in space and you throw a baseball in front of you, this action will cause an opposite reaction, moving you backwards

The same law which makes gun recoil happen. If you fire a pistol in vacuum you would still get the same recoil or even stronger. The rocket engine fires a lot of gas molecules instead of bullets at much higher velocity than a bullet, which gives it the constant push/recoil

Well the "super computer" argument is just not good because this wasnt an all purpose computer. This was specially build for this task. There are tons of special purpose chips today that wont be able to do general purpuse computing but crush a beefy pc in special tasks. Video encoding for example or tons of other tasks.

If you are actually arguing that our accomplishments in space aren't real, in good faith, you are very uneducated on the topic.

If the US made up the moon landing, we have many nations that have the technology to call out the lie. Yet none have, not even supposed 'enemies' of the US.

That one seems harder to 'work out', than your assumption that we couldn't go to space with the technology at the time.

People have even simulated the first moon landing using the same Apollo guidance code used in 1969. So there is a lot of evidence for anyone to work that one out.