Is this story set in a big city?

Does being an operator play into the story?

So, yes, there were operators working at night in the fifties, especially for international and long distance calling and also running the local exchange in smaller towns. Local exchanges in the larger cities were doing direct dial by the end of the fifties. A few small local exchanges stayed manual up to the early nineties.

It depends entirely where in the world the operator is (I'm assuming your story is set in the United States), and in how large a city or other settlement. By the late 1940s, many major cities in the United States, like New York and Chicago, and even medium-sized cities like Buffalo or Cleveland, had "round the clock" (as it was called) telephone service. However, many smaller towns and cities continued to have only daylight hours telephone service into the early 1960s, especially if the local exchange was operated by a smaller local telephone company rather than by Ma Bell (which was more common in rural areas and towns of 10,000 persons or less)

OP, in what location and size of settlement is your story taking place? It's impossible to give a precise and accurate answer without this information. Extant deployment of telephone technologies in the late 1940s and early 1950s varied greatly between urban and rural markets, with somewhat less variation regionally between urban markets depending on their size and location.