Rabbi Sorotzkin in Oznayim Latorah (Insights to the Torah) says that Noach continued to feed all the animals for the year after they left the teivah. In Noach 8:17, Hashem gives a bracha which includes the term שרצו which implies increasing like the "creeping things" (such as insects). Thus, Rabbi Sorotzkin says that immediately upon leaving the ark they began repopulating the world miraculously and being fed miraculously until there were enough to live as a balanced ecology.
Note that many animals have a minimum viable population size. Consider what happened to the passenger pigeons when the flocks were thinned below the critical level.
Also note that the flood lasted a full solar year and the normal lifespan of some species is less than that. This implies that "time" did not pass in the natural manner for the occupants of the Ark.
Rabbi Sorotzkin on 8:19 They came out of the Ark by their families
As Chazal note, this verse alludes to Hashem's command that the
animals not cohabit outside their species, and to the acceptance of
it. It also alludes to a special warning, stemming from the unique
situationin which all the animals found themselves upon leaving the
Ark. During the twelve months of their sojourn in the Ark, the
carnivorous birds and animals had refrained from violence; the lions
had eaten hay like cattle. This was achieved either by Noach placing
the carnivores and herbivores in separate rooms, "by their families",
or because even the animals and birds heeded Hashem's commands in
those terrible days (as they did in not cohabiting in the Ark), and
left their fellow animals in peace.
Now however, that they were leaving the Ark for freedom, if they were
to return immediately to their normal way of life, they would surely
wipe out some of the unclean species of which only two remained, one
male and one female, and the world would lose those species. They were
therefore commanded upon leavin to live for some time (at least twelve
months, the gestation period of the largest unclean beasts) "by their
families" - carnivores and herbivores separately - until all had a
chance to produce offspring. This obviated the fear that the world
would be left without some species created by Hashem.
