  The host galaxy conditions for rapid supermassive black hole growth are
poorly understood. Narrow-line Seyfert 1 (NLS1) galaxies often exhibit high
accretion rates and are hypothesized to be prototypes of active galactic nuclei
(AGN) at an early stage of their evolution. We present VLT MUSE NFM-AO
observations of Mrk 1044, the nearest super-Eddington accreting NLS1. Together
with archival MUSE WFM data we aim to understand the host galaxy processes that
drive Mrk 1044's black hole accretion. We extract the faint stellar continuum
emission from the AGN-deblended host and perform spatially resolved emission
line diagnostics with an unprecedented resolution. Combining both MUSE WFM and
NFM-AO observations, we use a kinematic model of a thin rotating disk to trace
the stellar and ionized gas motion from 10$\,$kpc down to 30$\,$pc around the
nucleus. Mrk 1044's stellar kinematics follow circular rotation, whereas the
ionized gas shows tenuous spiral features in the center. We resolve a compact
star forming circumnuclear ellipse (CNE) that has a semi-minor axis of
306$\,$pc. Within this CNE, the gas is metal rich and its line ratios are
entirely consistent with excitation by star formation. With an integrated SFR
of $0.19 \pm 0.05 \,{\rm M}_\odot\,{\rm yr}^{-1}$ the CNE contributes 27% of
the galaxy-wide star formation. We conclude that Mrk 1044's nuclear activity
has not yet affected the circumnuclear star formation. Thus, Mrk 1044 is
consistent with the idea that NLS1s are young AGN. A simple mass budget
consideration suggests that the circumnuclear star formation and AGN phase are
connected and the patterns in the ionized gas velocity field are a signature of
the ongoing AGN feeding.
