An energy density of 10^120 Joules per cubic metre (using m = E/c^2
this is 10^103 kg) corresponds to 10^52 kg (approximately the rest
mass of the universe as a whole) in a sphere of radius 10^-17
metres.So if space-time is curved very little, or not at all,at this
energy density,and given that the universe was extremely hot at the
outset,and so would probably have been able to expand with gravity so
weak,I conjecture that a classical calculation - not involving general
relativity - would show that our universe never got smaller than
10^-17 metres, and that such a calculation is valid.

Actually, this reasoning is incorrect, for the following 2 reasons
(which are connected).
Firstly, as is laid out in the FAQ, there is no universal definition
of energy in GR, such that it is conserved in integral form. That is,
locally energy is conserved in terms of flows, but integrated over the
universe where the curvature is global, it is not.

Secondly, when the Universe expands by scale factor L, the matter
density falls as L^-3, but the radiation density is Doppler-shifted,
so the radiation energy density scales as L^-4. The result is that in
the early Universe, it was dominated by the radiation energy density.
Which means that the total energy in the universe was much greater
than it is now.

The second argument suggests that it would be a closer approximation
taking the 3K microwave background, converting to an energy density,
and then scaling by L^4 to see when it hits the Planck energy density.
But I don't know whether detailed calculations would actually support
that either. Because the microwave background tells you what happened
when the radiation decoupled from matter as it de-ionised, and it is
much further still to a radiation-dominated universe