The laying season for geese is from mid February through to June/July. Traditionally they are supposed to start on Valentine's Day but my geese usually start a little later.
I have to ask, why just one egg? It is not a good idea to keep just one goose (or gander). In order to realistically hatch one gosling you would need to set at least 3 eggs or more. If you set the egg under a broody duck then, assuming it hatches, it would imprint on the duck, which would be fine for a while, but ultimately it would need a mate of its own size. If you intend to hatch the egg in an incubator the gosling will imprint on you - cute while its tiny but not so cute when much larger and wants to follow you everywhere.
I suggest you research keeping geese very carefully and then contact a reputable waterfowl breeder for some eggs around the end of April. Eggs take 30 days to hatch (approx) which means they will hatch when the weather is warming up.