Light welterweight Maxwell, who cut his teeth for the British Lionhearts in their first season in the World Series of Boxing, was drawn against Hungarian Mihai Nyeki in round one.
And he dominated from start to finish to win 3-0, taking every round on every judge's card, with Olympic bronze medallist Vincenzo Mangiacapre next up in Belarus.
Meanwhile Osueke, who also competed for the British Lionhearts in their debut WSB season, lost 2-0 to Peter Mullenberg of the Netherlands in their light heavyweight contest.
GB Boxing have sent a team of 13 to Minsk with Andrew Selby and Josh Taylor, both of whom competed for Team GB at the London 2012 Olympics, still to fight for the first time.
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- British Lionhearts