We know from Seymour's nickname for Muriel that the year is 1948. In later Glass family works, narrator Buddy Glass confirms that his brother Seymour committed suicide in 1948, allowing us to deduce that Seymour was 30 or 31 at the time.
It's interesting to consider the sort of dual setting we have in this story. The first half takes place in a hotel room indoors, where a sun-burnt Muriel talks on the phone to her mother. The second half takes place outside, in the sun and in the ocean, where a pale Seymour plays with young Sybil. It's appropriate that Muriel is indoors; she's materialistic and certainly less aware of the world (at least spiritually) than Seymour. It's also appropriate that Sybil and Seymour are outside, in the purity of the natural elements. It's striking that when Seymour enters the hotel room, he is immediately hit with the smell of "new calfskin luggage and nail-lacquer remover" (2.108). This world – the materialistic world of his wife – is very different than the pure, natural world he just occupied with Sybil.