A prequel would have to start out in the Sol system for its first season before stories could take place far away from the Sol system. To at least understand the context the main characters are established in.
- The last war among humans, on Mars, would be occurring at the turn of the century; the creation of the Fundamental Declaration of the Martian Colonies would be the likely outcome. The War for Martian Independence could possibly play a role in the origin story of the MACOs.
- Poverty, hunger & disease would still be present, though on the way out. Cancer would be cured at the start of the series with cytolytic injections. The Ozone would be either repaired or nearly repaired.
- Colonizing Alpha Centauri - which may or may not have an indigenous humanoid species living on the planet - would be a priority.
- Development of Jupiter Station would be another priority.
- The first freighter lanes being established (ex. Luna-Mars-Europa-Titan-Pluto-Alpha Centauri), with dilithium being the major commodity
- Unsolved murders by Redjac on Mars would spawn ghost stories, a freighter tradition.
- Lily Sloane would be a VIP due to her work and association with Zefram Cochrane. John Burke would be a VIP due to his work at the Royal Academy. Pyong Ko is either a VIP or memorialized for his work on cancer. A.E. Hodgkin would be in the early stages of developing Hodgkin’s Law in regards to parallel Earth and might be making his way to the Gagarin Radiation Belt. Henry Archer would still be an undergrad, possibly at Princeton University. Emory Erickson would be developing what becomes the transporter.
- Europe would be moving towards a European Hegemony and in turn a one world government, and would be rebuilding Paris among other European cities. Gaullists and Neo-Trotskyites might be political factions that still exist in Europe.
- The United States would still exist, and would be rebuilding NYC and DC, among US cities, and would be trying to retain influence in a multipolar world. There would be a reckoning in regard to its history in the 21st century (capitalist practices and anti-union practices, Sanctuary Districts, Second Civil War, Colonel Green’s eco-terrorists), though its advances in space exploration would be seen as a positive (Europa mission, Ares missions to Mars, development of warp drive). As would advanced in cybernetics (Jackson Roykirk). The US President in the series might be the African American female that is the fifth face on Mount Rushmore.
- The Eastern Coalition and the Pan-Caribbean government would still exist. Brazil would be building Amazon University. The Soviet Union might be reformed. Australia would be hyper nationalist and reluctant to join any world government at the start of the series. The United States of Africa might be already formed before the European Hegemony. Canada, Mexico, Venezuela, & Japan may have their own space agencies or be pushing for a global space agency.
- While early 21st century media & entertainment would be persevered, there would be lamentations of the loss of mid-21st century media & entertainment. Holographic entertainment would be in its infancy.
- The Royal Academy would be a major scientific institution as Earth rebuilds.
- 21st century neo-fascist factions would be on the way out and would be morphing into Earth First groups.
- Failed colonies would be commonplace (droughts, plagues, resource poor planets, natural disasters (comet/meteor strikes/solar flares), predators). Those that are successful are based around mining, scientific research, and/or archeology.
- No Earth ship goes faster than warp 2; sublight extremely common, there would be no anti-gravity, and ships/space stations would rely on cryogenics. Vulcan ships go to warp 7 and are the fastest ships in the known galaxy. Combined Human-Vulcan crews are very short lived. Humans would at least try to steal Vulcan state secrets to gain a level playing field in space exploration.
- Space modules with cryogenics would occasionally be discovered; with it being a struggle to integrate 20th and 21st century humans with the new 22nd century society.
- Vulcan establishing an embassy on Earth and debating permitting Earth to join the Interspecies Medical Exchange would be a huge arc.
In terms of aliens humans would encounter:
Unidentified pirates: Orions, Andorians, Tellarites, Mazarites, Osaarians, maybe Ktarians
Official first contacts: Denobulans, Ithenites, Rigelians, Nausicaans (first identified pirates), possibly Draylaxians, possibly Teneebians
Unofficially first contacts: Coridanites, Deltans, maybe Vissians, maybe Suliban, maybe Enolians
Known species: Vulcans, Kzinti
Romulans would also be in the series, clandestinely messing with Vulcan-human relations to create doubts, as well as disappearing humans cargo and colony ships by kamikazeing them.
I think the best way to make the first season exciting would be to take a Top Gun: Maverick approach.