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Yes, you can easily take the Vienna S-Bahn. The park advises that:
From the Danube’s south banks, use express train line S7 departing from Vienna (e.g. from Wien Floridsdorf, Praterstern or Wien Mitte), travelling in the direction of Wolfsthal. Stops include Maria Ellend, Haslau, Regelsbrunn, Petronell, and Hainburg.
The S7 also stops at the airport, so this should be a very easy connection. Service on the line runs at least hourly throughout most of the day, the journey will take as little as five minutes depending on which station you choose to go to, and the fare is (as of this writing) €4.90 one-way or €9.60 for a day ticket that will let you make the return trip. You can check the exact times and buy tickets on the ÖBB's website.
Do pay attention to the schedule, though, and make sure to leave enough time to get back from the park to the train station; if you are traveling during a part of the day when the trains are only hourly and you miss the one you need, you could have a very big risk of missing your flight.
The park's website also contains some information on recommended hikes in that part of the park.