Yes, you can play Sandbox from the start in JWE2. The only caveat is that you will not have all the maps to play with without playing the other modes. Otherwise, you have all the dinosaurs, buildings, and research at your disposal immediately after booting the game up. You can beat the Campaign in a couple of hours if you want a little variety in maps without putting in a lot of time outside of Sandbox.
Chaos Theory maps are unlocked at 3 stars for Jurassic Park, The Lost World, & Jurassic World. The very short and easy completions of Jurassic Park 3 and Fallen Kingdom net you those respective maps and these can be played in any order you like. Challenge Mode maps, if you really want those, are unlocked from having a cumulative number of stars across all maps, I recommend playing these all on Easy difficulty to get as many stars as possible so you can go back to Sandbox.