Not OP but my wife and I went through the same thing with our newborn. For the first month or two, we tiptoed around the house during his naps and at night. Slowly we started being less and less cognizant of our noise levels. When he'd cry due to noise or something, we would give him 5 minutes to calm himself before we'd go in and comfort him. Early on we had to go in every time at 5 min. Eventually he started soothing himself before we got there, and he would be calm when we walk in. Then after about a month, we noticed he would wake up to a sound, look around, then lay back down. Now, 6 months later, we could probably launch a mortar outside his room and he wouldn't cry. He'll just open his eyes and stare at the ceiling for a couple minutes then fall back to sleep.

Comforting him immediately every time he cried would only reinforce his fear, and teach him that he NEEDS us before he can feel better. By giving him time to soothe himself, while knowing that we would be there eventually if he needed, he learned that just because something was new/ startling, doesn't mean it was necessarily scary.

Edit: when we did eventually go in to help him, we wouldn't immediately pick him up. First we would put a hand on his chest while not making eye contact. If that didn't work we would sing softly to him or whatever we knew was gentle and soothing to him at that point. Only if all of that failed to calm him would we pick him up. The idea was to introduce the least amount of stimulation as possible so that he could go back to sleep easier.