= Solution
For an FLRW spacetime,
$$
R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}
=12\left[\left(\frac{\ddot a}{a}\right)^2
+\left(\frac{\dot a^2+k}{a^2}\right)^2\right].
$$
With $a=t$ and $k=-1$, both terms vanish, so
$$
\boxed{R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta}=0}.
$$
Indeed the vacuum equations give a vanishing Ricci tensor, and conformal flatness of an FLRW metric then makes the whole Riemann tensor vanish. The apparent singularity at $t=0$ is therefore only a coordinate singularity.
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