Even if we restrict ourselves to Morus rubra, the native species, versus Morus alba, the species introduced from China, and ignore possible hybrids, I think you may have to wait for the trees to be larger for an ID. I found a relevant paper (Nepal, M.P., M.H. Mayfield, C.J. Ferguson. 2012. "Identification of eastern North American Morus (Moraceae): Taxonomic status of M. murrayana." Phytoneuron 2012-26: 1–6.) which contains the following paragraph:
Salient features for correct identification of M. alba and M. rubra
Morus rubra can be easily distinguished from M. alba using
morphological characters of the leaf, bud, branch, bark and
infructescence. Leaf characters present a challenge because of the
tendency for leaves of juvenile shoots to converge in morphology among
these species. Nearly all of the unique characteristics of M. rubra
fail in juvenile leaves. Leaves of M. rubra (5–40 x 3–28 cm) are
larger overall than those of M. alba (2–20 x 1.5–18 cm). In M. rubra
leaves, the adaxial (upper) surface is rough and dull green (vs.
smooth and lustrous) and the abaxial (lower) surface is usually
densely hairy with erect trichomes evenly distributed (soft to the
touch); the base is often cordate (heart-shaped); the apex is acute,
acuminate to subcaudate; marginal teeth are often pointed; and the
color of the main veins is more or less like the color of the lamina
on the underside. Leaves of Morus alba are usually deep green and
lustrous adaxially and have few hairs concentrated along the main
veins on the abaxial surface; the base is rounded (vs. cordate); the
apex is obtuse; the marginal teeth are fewer, relatively larger, and
rounded; and the primary veins (underside) contrast more with the leaf
surface than in M. rubra. The winter buds of M. rubra have bud scale
margins with a darker (almost black) apical band, while in M. alba,
the bud scale margins are uniformly brown. Morus rubra has grayish
bark with flattened, thin plates that peel outwards in age. Morus alba
bark has thick and solid ridges that are more of a reddish tan
coloration. The orientation of branches in a mature M. rubra is
somewhat planar (flat) and spreading like an umbrella. In M. alba the
orientation of branches is more erect or spreading, and the plants
appear more rounded or bushy as a result. The fruit of M. rubra is
longer and narrowly cylindric, while in M. alba it is typically ovoid
This might be very useful for mature trees, but note the line "Leaf characters present a challenge because of the tendency for leaves of juvenile shoots to converge in morphology among these species. Nearly all of the unique characteristics of M. rubra fail in juvenile leaves."
There is also a recent, purely genetic analysis of the mulberries freely available at PLOS One but I don't think it's too helpful in this context other than it confirms that hybrids are common.
The Phytoneuron paper and a number of internet sites generally point to M. rubra being densely hairy on the underside of the leaves as one of the more important characters. Your specimens appear glabrous, but the pictures though excellent may still not show tiny hairs well. If we trust this character in the young plants then we would lean toward M. alba but as stated above, you may have to wait and see.