Globular clusters (GCs) formed when the Milky Way experienced a phase of rapid assembly. We use the wealth of information contained in the Galactic GC population to quantify the properties of the satellite galaxies from which the Milky Way assembled. To achieve this, we train an artificial neural network on the E-MOSAICS cosmological simulations of the co-formation and co-evolution of GCs and their host galaxies. The network uses the ages, metallicities, and orbital properties of GCs that formed in the same progenitor galaxies to predict the stellar masses and accretion redshifts of these progenitors. We apply the network to Galactic GCs associated with five progenitors: Gaia-Enceladus, the Helmi streams, Sequoia, Sagittarius, and the recently discovered, "low-energy" GCs, which we find to provide an excellent match to the predicted properties of the enigmatic galaxy “Kraken". The five galaxies cover a narrow stellar mass range (60-460 million solar masses), but widely different accretion redshifts (z=0.57-2.65). All accretion events represent minor mergers, but Kraken likely represents the most major merger ever experienced by the Milky Way, with a stellar mass ratio of 1:32 and a halo mass ratio of 1:7. Even though these progenitors likely were the Milky Way's most massive accretion events, they contributed a total mass of only a billion solar masses, similar to the stellar halo. This implies that the Milky Way grew its mass mostly by in-situ star formation. We conclude by organising these accretion events into the Milky Way's merger tree.