I didn't even notice that there was a third rail on both sides of one track. Yeah I would have to say late 1940's because by the 50's and eventually 60's those trees gradually disappeared along with that building with the dome on top.
View is looking East by the way, because the power lines at Amityville were always located on the North side of the ROW. From original, to temporary for grade crossing elimination, and today with it elevated.
The third rail next to the platform might be from a continuation from a freight siding since they were electrified as well.
This is the train to (NYC). Stopping at: Babylon, Lindenhurst, Copiague, Amityville, Massapequa Park, Massapequa, Seaford, Wantagh, Bellmore, Merrick, Freeport, Baldwin, Rockville Centre, Lynbrook, Valley Stream, Jamaica, Kew Gardens, Forest Hills, Woodside, Penn Station OR Grand Central.