Disclaimer: my team has a lot of manpower and decent in-house machining capability, so what works for us might not work for everyone else.
What my team does is after kickoff, where we make all our big strategy decisions (ex. tall vs short, priority list, etc.) we have “mechanism day” the next day. Here, we come up with every mechanism we can think of that could potentially be viable for the game, and decide which ones we want to prototype. We try and prototype everything that we don’t already have experience with and sometimes things we know how to build but need to fine-tune. For example, this year we came up with a bunch of manipulator prototypes, a shooter prototype because we needed to tune it, but only a handful of climber prototypes because for us, climbing on a bar is more or less a solved problem.
From there, we separate into groups to prototype each mechanism we decide is worth prototyping. We prototype until week 3, where we come back together as a team to figure out what ultimately goes on the robot. Once everyone’s reached a consensus, we start to CAD. CADing the robot and working out integration issues usually takes about a week, and we only start to order/machine parts once the entire robot CAD has been more or less finalized.
From there, which is usually around week 4, we start building. We build and wire the drivetrain first while mechanism leads work out the kinks in their mechanisms and get their stuff on the robot, which usually happens around week 5 or 6. Once we have a functional robot, we hand it off to programming and our drivers, who do their thing until our first competition. After competition, we iterate based on what we saw both during testing and at competition, and try to make all of our changes in time for our next event.
TLDR: Prototyping => CAD => build competition robot => competition => iteration