  Young massive clusters (YMCs) are the most massive star clusters forming in
nearby galaxies and are thought to be a young analogue to the globular
clusters. Understanding the formation process of YMCs leads to looking into
very efficient star formation in high-redshift galaxies suggested by recent
JWST observations. We investigate possible observational signatures of their
formation stage, particularly when the mass of a cluster is increasing via
accretion from a natal molecular cloud. To this end, we study the broad-band
continuum emission from ionized gas and dust enshrouding YMCs, whose formation
is followed by recent radiation-hydrodynamics simulations. We perform
post-process radiative transfer calculations using simulation snapshots and
find characteristic spectral features at radio and far-infrared frequencies. We
show that a striking feature is long-lasting, strong free-free emission from a
$\sim$ 10pc-scale HII region with a large emission measure of $\gtrsim 10^7
\mathrm{cm}^{-6} \ \mathrm{pc}$, corresponding to the mean electron density of
$\gtrsim 10^3~\mathrm{cm}^{-3}$. There is a turnover feature below $\sim$ 10
GHz, a signature of the optically-thick free-free emission, often found in
Galactic ultra-compact HII regions. These features come from the peculiar YMC
formation process, where the cluster's gravity effectively traps photoionized
gas for a long duration and enables continuous star formation within the
cluster. Such large and dense HII regions show distinct distribution on the
density-size diagram, apart from the standard sequence of Galactic HII regions.
This is consistent with the observational trend inferred for extragalactic HII
regions associated with YMCs.
