No matter of the type of the project: constructing a building, software, game, bridge, experience says you have few choices to avoid deadlines: build the most difficult things first (because at the start of the project you have plenty of time), then build the things that requires manpower (because you still have time), leave the things that can be quickly build and/or easy to integrate for later, when the time left for the project it not that much.
The approach above quickly deal with unforeseen issues, but requires that you have planned in advance the project and know all your tools and components, ie: game projects you need to understand the release for the engine strengths and its bugs to not get caught out of guard, acquired plugins need to be tested and known in advance, freeze upgrade on components that are already tested, because you can’t afford extra time to recover lost work later.
Big project teams can have different people working on different parts of same level. This is accomplished with level streaming where you have one map with landscape, another with illumination, another with props, and so on… they can all by loaded at same time composing a single level for playing. Check for perforce which is a versioning software and one of the best to work with game projects.