Is it possible to prepare for extreme stress while working as a first responder?

Yes, it is possible for first responders to prepare for extremely stressful situations. In fact, such occupations as police officers, firefighters, Emergency Medical Technicians (EMTs), and others train hard precisely to prepare for extremely stressful situations.
Professions such as those listed above are inherently stressful. Confronting armed suspects, or suspects who may or not be armed but who are encountered in a particularly tense environment, is extremely stressful, as is entering a burning building or attending to victims of a shooting while the shooter remains in the area. All of these are routine scenarios for which first responders prepare. 
Stress cannot be eliminated from inherently stressful scenarios, such as a terrorist attack or natural disaster. And, it is the exceedingly rare individual who is immune to the kind of stresses that can diminish the mental capacities of untrained individuals. That is why first responders train and train and train. They train because that is the only way they can be ready to respond to extremely stressful situations. That is why law enforcement academies include live fire ranges where recruits are subjected to different types of scenarios that require split-second decisions on whether to discharge their firearms. It is the reason firefighters attempt to recreate the most realistic training scenarios possible--so that prospective and active personnel will know how to respond if and when the scenarios depicted actually occur. And, it is why EMTs are incorporated into training exercises that involve large numbers of individuals who are enlisted into the exercises to act as "victims" of a shooting, airplane disaster, large-scale automotive accidents, and other possible contingencies. 
There is a problem with the training regimens described above, however. That problem is budgetary. Training costs money, and the more specialized the training, or the more elite the unit, the higher the costs. Plus, training takes time—time not spent on the street patrolling, for instance. Consequently, not every department with first responders is as well-prepared as circumstances may dictate. This, however, is a bit of a digression. First responders can be prepared for extreme stress. That preparedness comes from training in real-life scenarios, including on mock-ups of actual city streets or buildings into which first responders will likely have to enter under difficult circumstances. Pay a visit to a modern law enforcement academy, or the one operated by the United States Secret Service or the Federal Bureau of Investigation, and you will observe recruits and others being subjected to real-life, extremely stressful scenarios in fake towns designed to simulate the kinds of situations they may have to face during the course of their careers.
https://www.fbi.gov/services/training-academy