  The turbulent small-scale dynamo (SSD) is likely to be responsible for the
magnetisation of the interstellar medium (ISM) that we observe in the Universe
today. The SSD efficiently converts kinetic energy $E_{\rm kin}$ into magnetic
energy $E_{\rm mag} $, and is often used to explain how an initially weak
magnetic field with $E_{\rm mag} \ll E_{\rm kin}$ is amplified, and then
maintained at a level $E_{\rm mag} \lesssim E_{\rm kin}$. Usually, this process
is studied by initialising a weak seed magnetic field and letting the
turbulence grow it to saturation. However, in this Part I of the Growth or
Decay series, using three-dimensional, visco-resistive magnetohydrodynamical
turbulence simulations up to magnetic Reynolds numbers of 2000, we show that
the same final state in the integral quantities, energy spectra, and
characteristic scales of the magnetic field can also be achieved if initially
$E_{\rm mag} \sim E_{\rm kin}$ or even if initially $E_{\rm mag} \gg E_{\rm
kin}$. This suggests that the final saturated state of the turbulent dynamo is
set by the turbulence and the material properties of the plasma, independent of
the initial structure or amplitude of the magnetic field. We discuss the
implications this has for the maintenance of magnetic fields in turbulent
plasmas and future studies exploring the dynamo saturation.
