Was it possible for my father to live and for his destiny to change had he been transported to the hospital earlier, immediately upon feeling pain, or was his death inevitable?

May Allah have mercy on your father. You must strive to honor him and do good to him after his death by giving charity on his behalf and supplicating for him. Any act of devotion for which you dedicate the reward to him will benefit him. As for your responsibility for what happened, it appears that you were not negligent, and no one is responsible for what occurred, as it was Allah's decree. Abandon worry and self-blame, for Allah alone knows what would have happened had you taken him to the hospital earlier.