You can hike or bike a sandy forest road from Marcinkonys (where the reserve has a museum) (~5 km), which will bring you to the western edge of the swamp.
There’s a viewing tower atop a high dune, and from there you will be able to scan a broad territory. There’s a 1.5 km trail right there with a viewing platform atop the swamp. For more information: www.cepkeliai.lt (only in Lithuanian).