Here is the New York Times’ box score for the New York Highlanders’ first game, on April 22, 1903, played vs. the Washington Senators/Nationals in D.C.:
The game account, in two parts:
A couple things to note: the Highlanders started play in New York at Hilltop Park in north Manhattan. Willie Keeler, Jack Chesbro, and Clark Griffith were the team’s three players (Griffith also managed) who people might recognize now. In 1901 and 1902, they were the Baltimore Orioles.
Also, as a coda, here is a December 1902 story confirming that the Orioles were going to move to New York City for the 1903 season-note the nice “Little Actual Business Done” part of the headline: