This advice is a good first read on the political elements before you make a real move, but it’s not a plan, and it sounds like a recipe for mediocrity. (Not that there is anything wrong with that)
If you actually want to have some integrity when you talk about deadlines before it eats up your insides and you lose sleep you will need to have these beer / lunch conversations to gauge the level of appetite for change and then start talking about how to get something shipped on time as well as the consequences for not shipping on time.
Sounds like you already have this dialog with your manager. Keep talking about how best to manage expectations up the chain.
You’ll want to get buy-in to reduce scope or make whatever other changes you need, otherwise you’ll have to lie to keep up the facade that things will ship on time. It will burn you out.
If the read in the parent comment is bad for your org and it’s NOT normal to BS deadlines and ship late then no paper trail or written warnings, risks, and issues brings with it some badness as well - judge for your organization. I’m guessing you may already know the answer.
This is probably not the best career ladder advice at some firms, but at all costs make sure you never lie for anybody. Keep your integrity. Be honest. Sleep at night.
Of course sometimes “honest” is an excuse to be pessimistic. Look hard to make sure your dire warnings are not “chicken little” pessimism, then talk it out with your management, but don’t lie for them and be honest about your engineering and your team.