Well, seniority helps on the deadlines front: you can spot managers trying to force too short deadlines on you a mile away and throw it back at them (“I’m am the specialist, so I’m the one who knows best how long it will take”) and if they just try and impose deadlines you can bluntly state “that isn’t possible” and if they somehow have the authority to push them you make sure everybody (especially other managers, ideally the managers above them) knows that you’ve informed them upfront that such deadlines were impossible so when it inevitably fails, said manager can’t shove the blame your way.

As for obtaining things from other teams, that’s a two part thing:

• First make it painfully obvious in your estimates that a dependency on something from an outside teams exists. When inquired about progress, constantly point out that it will only happen “if that team provides us what we need to progress”. Keep reminding people that those deliverables are a conditional for yours - “they’re late our project is late”.
• Second, start pushing them for delivering to you what you need well before you need it. It’s there, in your planning, so you know you need it and have some idea of when. The bigger the project the earlier you start pestering them. Persist on asking them for it, escalate to upper management if no movement is visible on their side. Make sure the groundwork is set so that if they’re late they get the blame on project deadlines being missed. It depends on the country culture but generally most people aren’t really impeccable professionals at time and priority management (and yeah, that includes managers) and tend to prioritize addressing “what’s burning harder” in their pile, hence why you need to start pestering them early, do it often and with more urgency the closer it gets to the point you need it (to make sure it’s perceive as an urgent need and rises to the top of their priority pile) and make sure the groundwork is set for them to be blame if your own deadline is missed because they were late and, more importantly, that THEY know they will get the blame (this generally at mid/upper manager level), so that from their point of view it’s “burning” (i.e. they’ll suffer if that doesn’t get picked up on time)

Of course, all this requires competent management since they’re the ones supposed to do it and if your managers are trying to impose deadlines on you or using slimy trickery to get people to commit to shorter deadlines, they’re NOT competent managers - that kind of shit invariably yields death marches and bug-riddled results that in the mid and long term end up wasting far more time that it was shave by those shorter deadlines.

Kinda sad that one has to play such games. Welcome to Mankind.