At my first job part of my responsibilities was answering the phone. For me it worked to start talking before I actually pick up the phone. I heard the signal, I started repeating "hello" and then answer. It helped me to ease into the conversation (I usually don't stutter when talking to myself). Also it helped me to say 1st phrase when I was going to call someone. On some point I discovered that not having a good posture is also helpful for me. So I answered the phone leaning to the wall or sitting on one leg. I guess having some of the muscles relaxed helped me to relax my throat as well. I use some of these tricks now talking via zoom now or to start conversation with shop assistants etc.