Timashov, a native of Kirovograd, Ukraine, developed into a top prospect playing in Sweden. He came to North America in 2014-15 to play for Quebec of the Quebec Major Junior Hockey League and led the league's rookies with 90 points (19 goals, 71 assists) in 66 games. The Toronto Maple Leafs selected him in the fifth round (No. 125) of the 2015 NHL Draft.
He split 2015-16 between Quebec and Shawinigan, then joined Toronto of the American Hockey League in 2016.