Working under pressure is my job in a nutshell. The Navy trained me to make all of my decisions as if they needed instant responses. I tend to use a quick assessment process that we know as I AM IS. Its an acronym.
Identify hazard/problem
Assess nature/severity
Make risk decisions
Implement controls
Supervise
My mindset is to tackle the problem by questioning it. Will this problem be easily mitigated in the time required? Will this problem exaggerate with time? Can this problem be isolated to mitigate without affecting its surrounding environment? Does the problem warrwnt halting operations in the surrounding environment, and will that come at a high detriment to the workplace? Do I need an administrative control approach or a physical approach?
If you tend to get too many thoughts in your head when approaching a situation under pressure, the best you can do is isolate the factors surrounding the problem and tackle the key factors first. We tend to default to what we learned in training when under pressure, like muscle memory. So the best you can do to adapt to pressure is to find the mindset you work the best with, and practice engaging that mindset on a moment's notice. Plan for the worst, so the shock doesn't kick in when a situation arises and you can approach it with a cool head. If you ever have questions regarding time critical risk management, I have some training resources I can send you. Just reach out to me.

What type of pressure are we talking about? Is it making decisions under time pressure where we need an answer immediately? Or is the pressure related to the gravity of the decision to be made not time pressure?

If time pressure is not a problem, then using a classical decision-making process such as bounded rationality is probably the best. When we have time to collect data, analyze it, develop possible solutions and choose the best solution, then we should do it.

Making decisions under time pressure is a very different process. Usually, decisions made under time pressure use a pattern matching algorithm. In the late 80s, Gary Klein studied decision-making of firefighters and NICU nurses. What he found was that experts make decisions very differently when the decision must be made quickly. He developed the recognition-primed decision-making model to describe this process. It is important to understand that the ability to make correct decisions under time pressure requires extensive expertise. Klein outlines this research in his book Sources of Power. This book is a must read for anyone involved in decisions under time pressure.

So what if you have to make an important decision under time pressure, but you are not an expert. Danny Kahneman and Amos Tversky's research shows us that you will probably use a heuristic (a short cut) to make the decision. One example of a heuristic is substitution. You use the substitution heuristic when you substitute an easier problem for a more complex problem. The problem with heuristics is that they can lead to errors. Kahneman explains these issues in his book Thinking Fast and Slow. Another book all safety professionals should read.

I have experience as a first responder so I guess making decisions under pressure comes naturally to me now. I think ultimately you have to use the knowledge you have about safety first then weigh the business impact. When you are under pressure to complete something or make a decision it's important to just slow down and think about how to stay on track. Think about the end goal and what steps you can take to achieve it. Writing things down or keeping a task planner helps me stay on tracks with the steps I need to complete for projects. In terms of making pressured decisions on the spot, just keep ethics in mind. Make decisions based on your duty to keep employees safe. In my experience with manufacturing there have been many times that I have had to stop work due to unsafe conditions or decisions management had made to cut corners. It is not easy to tell someone to stop what they are doing, especially when it interferes with time-sensitive projects. I have also been put in a situation where I have had to observe processes that I felt were unsafe, but at the time there was not a safer alternative. In instances like these I have recorded my observations and watched closely to ensure none of my employees were being put in imminent danger, then following the event we would debrief and I would offer suggestions to management to make the process safer.

I have two approaches if I am struggling to find confidence when pressured by an employee at work. The first is when I do not have a reference immediately available. In this case, I simply inform them of my stance but I will have to get back to them. When I do have references for my ground, I re-state the question/concern, mention the regulatory requirement (if applicable), then the internal business rule (if applicable), then the best practice. Having at least one of those explanations usually wins the argument for health- and safety-related items.