Chemical rockets were a highly inefficient and primitive method of getting into space. In the late ancient 21st century, ancient space debris has indicated that much more efficient ways of getting into space were invented, such as sky hooks, space elevators and space planes with hybrid jet-ion engines.
In order to get to space using chemical rockets, you need a skyscraper sized rocket to be moved to a launchpad that uses special equipment to keep the pad cool, and to keep the extreme noise from damaging anything nearby.
Once the rocket gets high enough, workers came up with the idea to ditch empty tanks and atmosphere-type engines, so that the upper part of the rocket with engines better for propulsion within a vacuum can lift the upper stage to orbit.
By the time orbit is achieved, people would regularly lose 3/4th of the rocket. Without the ability to zip anywhere with warp drives, complicated maneuvers had to be executed to change the orbit to, say, intersect a planet or damaged satellite.
In the ancient 21st century, rocket debris has undergone some changes, the main one that they're a lot less damaged when archaeologists dug them up. The changes, such as reignitable engines, indicate that rockets were able to fly back to the launch zone, instead of letting debris fall and get destroyed. Occasionally, boosters would fly back to a barge for reuse. Assuming economics worked the same way, this reduced costs.
Despite the combined effort of thousands of archaeologists working around ancient launch zones, it is unknown how non reusable stages were handled after separation. Some theories suggest that the boosters were ditched over enemy countries due to lack of peace before a Type I civ was achieved by Humanity. Others suggest that ditched stages were blown up when a safe distance was reached.
Currently, there have been no reconstructed images of these ancient rockets.