We study first-passage time (FPT) distributions of target finding events through complex environments with elongated obstacles distributed with different anisotropies and volume occupation fractions. For isotropic systems and for low densities of aligned obstacles, FPTs are exponentially distributed. At large enough densities of aligned obstructions, elongated channels emerge, gradually reducing the dynamics dimensionality from 3D in the case of broad geometries, to 1D in the case of narrow structures. We analyze how the local structure of the channels, such as geometry and size, modifies the FPT distribution. Because of the complex nature of fibrous biological environments in tissues, we suggest that our results shed light on the understanding of the molecular transport accruing between cells.