We describe a polymer‐supported stereoselective synthesis of the (1S,5S)‐6‐oxa‐3,8‐diazabicyclo[3.2.1]octane‐bridged scaffold by tandem iminium ion cyclization/nucleophilic addition reactions. A series of resin‐bound acyclic intermediates bearing different substituents were prepared, and the scope and limitations of the chemical route leading to the bridged scaffold were evaluated. The Thr‐derived bridged scaffold was found to be substantially more stable in acid than the Ser‐derived scaffold, which was partially transformed into dihydropyrazinones. Substitution at the iminium‐forming nitrogen was critical for acid stability, and the N‐arylsulfonamides with electron‐withdrawing groups yielded the highest purity of the crude products prepared by acid‐mediated cleavage. The acid‐labile target compounds were synthesized by nucleophile‐mediated cleavage from the esterified Wang resin and cyclization in formic acid.