  The ALMA-IMF Large Program provides multi-tracer observations of 15 Galactic
massive protoclusters at matched sensitivity and spatial resolution. We focus
on the dense gas kinematics of the G353.41 protocluster traced by N$_2$H$^+$
(1$-$0), with an spatial resolution $\sim$0.02 pc. G353.41, at a distance of
$\sim$2 kpc, has a mass of $\sim$2500 M$_{\odot}$ within $1.3\times1.3$ pc$^2$.
We extract the N$_2$H$^+$ isolated line component and we decompose it by
fitting up to 3 Gaussian velocity components. This allows us to identify
velocity structures that are impossible to identify in the traditional
position-velocity diagram. We identify multiple velocity gradients on large
($\sim$1 pc) and small scales ($\sim$0.2 pc). We find good agreement between
the N$_2$H$^+$ velocities and the previously reported DCN core velocities,
suggesting that cores are kinematically coupled to the dense gas in which they
form. We measure 9 converging ``V-shaped'' velocity gradients ($\sim20$
km/s/pc), located in filaments, which are sometimes associated with cores near
their point of convergence. The average inflow timescale is $\sim67$ kyr, or
about twice the free-fall time of cores in the same area ($\sim33$ kyr) but
substantially shorter than protostar lifetime estimates ($\sim$0.5 Myr). We
derive mass accretion rates in the range of $(0.35-8.77)\,\times\,10^{-4}$
M$_{\odot}$/yr. This feeding might lead to further filament collapse and
formation of new cores. We suggest that the protocluster is collapsing on large
scales, but the velocity signature of collapse is slow compared to pure
free-fall. These data are consistent with a comparatively slow global
protocluster contraction under gravity, and faster core formation within,
suggesting the formation of multiple generations of stars over the protocluster
lifetime.
