The Kuqa fold-thrust belt arguably hosts Earth's highest density of diverse surface salt structures, including salt-cored anticlines, strike-slip faults that double as salt walls, salt domes, and salt thrusts. Key aspects of the structural development of the range are unresolved. In particular, it is unclear whether the fold-thrust belt developed via forward-propagating salt-cored detachment folds which locally nucleated late thrust faults, or if such detachment folds grew interspersed with either (i) long-lived pre-kinematic salt diapirs that evolved into local salt thrusts and/or (ii) source-fed thrust faults and associated folds. Detachment folds and hanging wall anticlines of source-fed thrusts feature gradual lateral propagation during growth, whereas diapirs either lack lateral propagation or involve irregular propagation and dramatic strain gradients. Therefore, we test the hypotheses by examining potential geomorphological records of lateral ridge propagation along the frontal Kuqa fold-thrust belt. A particular focus is the Quele salt thrust, because it spans one tenth of the length of the frontal belt and it is commonly hypothesized to represent a deformed diapir or a source-fed thrust fault. We find that all ridges along the frontal Kuqa fold-thrust belt feature (1) bow-shaped along-strike topography, with decreasing relief from the topographic crest to the plunging ends of the ridges, (2) curved wind and water gaps, (3) asymmetric fan-shaped and forked-shaped tributaries, and (4) drainage basin maturity decreases towards lateral ridge terminations. These features are consistent with lateral fold propagation. At the Quele salt thrust, such evidence indicates that the hanging wall developed as two distinct anticlines which merged into a composite anticlinorium. Our findings indicate that the frontal Kuqa fold-thrust belt developed either by detachment folding with local late thrust fault formation, or via such structures interspersed with source-fed thrust faults.