He began taking piano lessons at the age of 4 and in 2006 he graduated from Los Angeles County High School for the Arts.

He studied composition with Stephen Hartke, Donald Crockett, Frank Ticheli, and Steven Stucky, and piano with Benjamin Pasternack and Stewart L. Gordon.

[4] Kotcheff has held residencies at Festival International d'Art Lyrique d'Aix-en-Provence,[5] the Los Angeles Philharmonic's National Composers Intensive,[6] The Hermitage Artist Retreat,[7] The Studios of Key West,[8] and The Kimmel Harding Nelson Center for the Arts.

[19] Together with composer Ludwig Göransson, he co-wrote the tracks "Trinity" and "Something More Important" on the soundtrack of the 2023 film Oppenheimer by Christopher Nolan.

Together with composer Kris Bowers, he co-wrote the tracks "William Gracey", "It's Happy Hour Somewhere", and "Ghost Chase" on the soundtrack of the 2023 film Haunted Mansion by Justin Simien.