Television

The show can see the future, which helps the early seasons a lot. Knowing what happens in the later books allows them to bring stuff forward. A great example of this is in the pilot when Avasarala is torturing a Belter and questioning him about stolen stealth tech. This is a character that doesn't even appear in the first book and it is setting things up that don't become important until book/season 4/5.

The authors being active writers on the show and senior producers on the later seasons also helps. They aren't in charge, which means people with TV experience make the show work, but they keep the voice consistent. Regardless of who is credited as writer on an episode, nearly all Amos stuff in the first two seasons is written by one of the authors so that his mentality would be consistent. Throughout the whole run of the show, pretty much all the formal speeches are written by the other author.

The last thing that really helps them is the drive to be faithful to the story of the source without being slave to it. This leads to many small changes that slot actors they already have into story beats, giving the viewer more connection to what they see. Drummer, for example, is a tiny character in the books but the actress was great so they kept slotting her in instead of having a different Belter for everything. She even erased the existence of a main POV character and took on that role, outlived his role and just kept going. That then leaves his character design available, so he ends up being a major character in season 5, a completely different book.

We can thank Game of Thrones for a lot of that. One of the authors worked for GRRM for a while and was involved in his side of the early seasons of GOT. Even early on when it was well received, GRRM was getting frustrated by the changes the show was making without regard to knock-on effects. When selling the TV rights for Expanse, they fought to be in the room for both writing and production so that they could have a say when decisions were being made as opposed to just being asked for feedback after the fact.