We express the scalar four-point correlator of the $Q$-model associated with the proposed minimal higher-spin dS/Sp($N$) correspondence as an integral over the orthogonal Grassmannian OGr(4,8). The full, crossing-symmetric Higher-Spin Grassmannian correlator is given by $(S^2+T^2+U^2)/(STU)$, where $S$, $T$, $U$ are the Grassmannian Mandelstam variables. Remarkably, this has the same form as the field-theory limit of the Veneziano amplitude, despite encoding an infinite massless higher-spin tower associated with the opposite, tensionless regime. For the scalar sector considered here, the Grassmannian contour gives the full correlator, with no dispersive reconstruction required. We verify the formula by evaluating the contour integral and matching it to the complete momentum-space result, and analyze its singularities and higher-spin residues directly in Grassmannian space.