[4] Despite two standout seasons with TPS showing developmental promise, Georgiev went undrafted through the 2017 NHL entry draft.

With an ambition to play in North America, Georgiev was invited to participate in the New York Rangers' developmental camp.

[7] On 3 March, Georgiev stopped 35 shots and earned his first NHL win as the Rangers beat the Edmonton Oilers 3–2.

[9][10] In a 3 March game against the Washington Capitals, Georgiev threw his stick at the puck after forward Alexander Ovechkin had faked him out.

[12] As a pending restricted free agent he quickly agreed to terms on a three-year, $10.2 million contract with the Avalanche on 10 July 2022.