When something begins in a way that makes you think it will go well later, it starts promisingly. You are naming the early signs — a first match, a first lesson, the opening of a year — not the ending. A job can begin promisingly and still turn difficult; the word allows that. Teachers and newspapers like it; it feels a little more careful than “well” or “nicely.” Though actually, it is not the same as making a promise. Nobody is giving their word. They are only saying the first clues look good.