The only child of a Viennese mother and a Serbian father, both of whom worked as translators, Paich led a dramatic and unconventional life. As a child in Belgrade, Yugoslavia, Paich performed in radio, television, and film productions, which included a leading role in the film Prozvan Je i V3.. At age sixteen, while attending the Academy of Fine Arts, Belgrade, Paich began to organize independent, avant-garde community theater groups. After he was warned that his collaborations with artists and intellectuals who were working to start an alternative political party might lead to his incarceration, in 1967, at the age of nineteen, Paich escaped Yugoslavia and immigrated to Great Britain.

After working as an icon painter in London, Paich met Joan Littlewood, who invited him to work with her on avant-garde projects around London and Liverpool. After winning the first place award at the 1973 GREP (Groupe de recherche et d'education pour la promotion) International Architectural Competition in Paris, Paich was invited to chair and direct the Fano Foundation Educational Village and International Summer School in Apulia, southern Italy. At the Fano Educational Village's summer school, Paich and five other instructors from England taught traditional arts and community living practices that continued consecutive summers between 1975 and 1980. In 1980, Paich was admitted to the Royal College of Art, where he graduated with an MFA degree in 1983. During his time at the Royal College, he represented England at the Venice Biennale. Paich lived and worked in London until 1985, where he taught various studio art courses, Architecture, and the History of Art and Ideas at several post-secondary schools in London and also lectured at the Glasgow School of Art.