Moire superlattices(1,2) have recently emerged as a platform upon which correlated physics and superconductivity can be studied with unprecedented tunability(3-6). Although correlated effects have been observed in several other moire system(7-17), magic-angle twisted bilayergraphene remains the only one in which robust superconductivity has been reproducibly measured(4-6). Here we realize a moire superconductor in magic-angle twisted trilayer graphene (MATTG)(18), which has better tunability of its electronic structure and superconducting properties than magic-angle twisted bilayer graphene. Measurements ofthe Hall effect and quantum oscillations as a function of density and electric field enable us to determine the tunable phase boundaries of the system in the normal metallic state. Zero-magnetic-field resistivity measurements reveal that the existence of superconductivity is intimately connected to the broken-symmetry phase that emerges from two carriers per moire unit cell. We find that the superconducting phase is suppressed and bounded at the Van Hove singularities that partially surround the broken-symmetry phase, which is difficult to reconcile with weak-coupling Bardeen-Cooper-Schrieffer theory. Moreover, the extensive in situ tunability of our system allows us to reach the ultrastrong-coupling regime, characterized by a Ginzburg-Landau coherence length that reaches the average inter-particle distance, and very large T-BKT/F, values, in excess of 0.1 (where T-BKT and T-F are the Berezinskii-Kosterlitz-Thouless transition and Fermi temperatures, respectively). These observations suggest that MATTG can be electrically tuned close to the crossover to a two-dimensional Bose-Einstein condensate. Our results establish a family of tunable moire superconductors that have the potential to revolutionize our fundamental understanding of and the applications for strongly coupled superconductivity.