= Solution
The <Christoffel symbols of a spatially flat FLRW metric> depend on the time-coordinate convention. Here $x^0$ is $t$, not $ct$. For an <affine parameter> $\lambda$, take $\mathcal L=\tfrac12[c^2\dot t^2-a^2(t)\delta_{ij}\dot x^i\dot x^j]$. Its <Euler-Lagrange equations> are
$$
\ddot t+\frac{aa'}{c^2}\delta_{ij}\dot x^i\dot x^j=0,\qquad
\ddot x^i+2\frac{a'}a\dot t\dot x^i=0.
$$
Comparison with the <geodesic equation> gives
$$
\boxed{\Gamma^0{}_{ij}=\frac{aa'}{c^2}\delta_{ij},\qquad
\Gamma^i{}_{0j}=\Gamma^i{}_{j0}=\frac{a'}a\delta^i{}_j}.
$$
All others vanish because $g_{00}$ is constant and there are no spatial <metric tensor> <derivatives>. The lower-index interchange is essential: the printed list specifies one member of each symmetric mixed pair. The factor of two in the spatial <geodesic equation> comes from those two members.
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