Context. Massive early-type galaxies are believed to be the end result of an extended mass accretion history. The stars formed in situ very early on in the initial phase of the mass assembly might have originated from an extremely intense and rapid burst of star formation. These stars may still be found within the cores of such galaxies at z=0, depending on their accretion and merger histories.Aims. We wish to investigate the presence of a surviving high-z compact progenitor component in the brightest galaxy of the Hydra I cluster, NGC 3311, by mapping its 2D kinematics and stellar population out to 2 effective radii. Our goal is to understand the formation of its several structural components and trace their mass assembly back in time.Methods. We combined MUSE observations, a customized and extended version of the state-of-the-art EMILES single stellar population models, and a newly developed parametric fully Bayesian framework to model the observed spectra using full-spectrum fitting.Results. We present 2D maps and radial profiles of the stellar velocity dispersion, age, total metallicity, alpha -element, sodium abundance ([Na/Fe]), and the initial mass function (IMF) slope. All properties have significant gradients, confirming the existence of multiple structural components, also including a "blue spot" characterized by younger and more metal-rich stars. We find that the component dominating the light budget of NGC 3311 within R less than or similar to 2.0 kpc is the surviving z=0 analog of a high-z compact core. This concentrated structure has a relatively small velocity dispersion (sigma (*)approximate to 180 km s(-1)), is very old (ages greater than or similar to 11 Gyr), metal-rich ([Z/H] similar to 0.2 and [Na/Fe] similar to 0.4), and has a bottom-heavy IMF (with slope Gamma (b)similar to 2.4). In the outer region, instead, the line-of-sight velocity distribution becomes increasingly broad, and the stars are younger. They are also more metal and sodium poor but are richer in alpha -elements. The low-mass end of the IMF slope becomes Chabrier-like with increasing galactocentric distance.Conclusions. The existence of multiple structural components in NGC 3311 from photometry, kinematics, and stellar populations confirms the predictions from the two-phase formation scenario for NGC 3311, according to which a first very short, high-z star-formation episode formed a compact stellar structure in its core, which then grew in size by the extended mass assembly of relatively massive satellites. Interestingly, the outer stellar population has an overabundant [alpha /Fe], most likely because NGC 3311, located at the center of the galaxy cluster, accreted stars from rapidly quenched satellites.