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With world number one Ash Barty opting out of the tournament due to the coronavirus, Ajla Tomljanovic assumed top-ranked status among her fellow Australian entrants.
However, the 27-year-old was unable to find a way past 2016 champion Angelique Kerber, going down 6-4 6-4.
Lizette Cabrera also struggled in just her second appearance in the main draw, with Danka Kovinic emerging victorious in three sets, 6-4 3-6 6-2.
Maddison Inglis and Arina Rodionova soon joined the 22-year-old, failing against Magda Linette and Madison Brengle respectively.
Astra Sharma meanwhile took 19th seed Dayana Yastremska to a third-set tie-breaker, before bowing out 6-3 6-7 7-6 in New York.
Jordan Thompson was the only Australian to emerge victorious from the first round, seeing off Italian Stefano Travaglia in four sets, 6-3 6-4 4-6 6-2.