Andrey Makarov was born on April 20, 1993 in Kazan, Russia. A standout goaltender in his homeland, he played his major junior hockey with the Lewiston Maineiacs of the QMJHL and the Saskatoon Blades of the WHL. Makarov was awarded the Hap Emms Memorial Trophy as the most outstanding goaltender at the 2013 Memorial Cup. In 115 career WHL games with Saskatoon, Makarov went 66-38-7 with a .916 save percentage, a 2.80 goals-against average, and nine shutouts. Undrafted into the NHL, he signed as a free agent with the Buffalo Sabres.
On the international stage Makarov represented Russia 2012 and 2013 World Junior Championships, winning silver and bronze respectively.
Makarov made his professional debut on November 1, 2013 with the Fort Wayne Komets of the ECHL. In all he would play 31 games for the Komets during the 2013–14 season, posting a record of 15-11-4, with a .906 save percentage and a 2.79 goals-against-average. He was recalled to the Rochester Americans of the American Hockey League and would subsequently receive his first NHL call-up on April 8, 2014. He would appear in a single game for the Sabres, making 33 saves on 36 shots.