Governments and development partners often seek Sustainable Development Goal (SDG) "accelerators" whose progress can propagate gains across human well-being, institutions, resources, and environmental priorities. Such claims require evidence on direction, timing, robustness, and trade-offs, not only network connectivity. We map directed SDG interdependence using a balanced panel of 114 countries observed annually from 2000 to 2024. Because the goal series are persistent, trending, and cross-sectionally dependent, we combine Dumitrescu-Hurlin panel Granger non-causality tests on first-differenced series with false-discovery control across 272 directed goal pairs, and panel local projections with Driscoll-Kraay standard errors for 31 theory-derived indicator linkages. We find 84 directed linkages after correction: 40 synergies and 44 trade-offs. This dense structure does not support a universal accelerator. Driver-receiver rankings are fragile across lag orders, centrality metrics, bootstrap resampling, and alternative dependence controls; only peace and strong institutions as a net receiver and poverty reduction as an effect-size-weighted driver are distinguishable in the bootstrap screen. Two local-projection pathways are supported, both leading to lower child mortality, and the education-child-health association is corroborated in independent World Development Indicators data across 183 countries. The policy implication is not to abandon SDG integration, but to replace fixed global accelerator rankings with adaptive portfolios built around supported, time-lagged linkages and monitored constituent indicators.

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