I saw a user on Boardgamegeek talk about only going with the Prelude to Woodbury expansion to start his collection in The Walking Dead: All Out War and never picking up the Core Set. I think this is perfectly doable but like in most things, there will be tradeoffs and balances to this approach.
I decided to research more into this and find out exactly what you’ll be missing if you go this route and what do you gain.