A population of >6 million people worldwide at high risk of Alzheimer's disease (AD) are those with Down Syndrome (DS, caused by trisomy 21 (T21)), 70% of whom develop dementia during lifetime, caused by an extra copy of β-amyloid-(Aβ)-precursor-protein gene. We report AD-like pathology in cerebral organoids grown in vitro from non-invasively sampled strands of hair from 71% of DS donors. The pathology consisted of extracellular diffuse and fibrillar Aβ deposits, hyperphosphorylated/pathologically conformed Tau, and premature neuronal loss. Presence/absence of AD-like pathology was donor-specific (reproducible between individual organoids/iPSC lines/experiments). Pathology could be triggered in pathology-negative T21 organoids by CRISPR/Cas9-mediated elimination of the third copy of chromosome-21-gene BACE2, but prevented by combined chemical β and γ-secretase inhibition. We found that T21-organoids secrete increased proportions of Aβ-preventing (Aβ1-19) and Aβ degradation products (Aβ1-20 and Aβ1-34). We show these profiles mirror in cerebrospinal fluid of people with DS. We demonstrate that this protective mechanism is mediated by BACE2-trisomy and cross-inhibited by clinically trialled BACE1-inhibitors. Combined, our data prove the physiological role of BACE2 as a dose-sensitive AD-suppressor gene, potentially explaining the dementia delay in ~30% of people with DS. We also show that DS cerebral organoids could be explored as pre-morbid AD-risk population detector and a system for hypothesis-free drug screens as well as identification of natural suppressor genes for neurodegenerative diseases.