What species of mulberry is this?
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
  or ellipsoid.


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.