We present progress in a lattice QCD study of the electromagnetic and axial $N\to\Delta(1232)$ resonance transition form factors. Our long-term aim is to apply the Lellouch-L\"uscher
formalism to extract infinite-volume $N\to N\pi$ form factors from finite-volume matrix elements. We previously computed the required $N\pi$ scattering amplitudes on an ensemble with $N_f=2+1$ clover fermions at $m_\pi \approx 255$ MeV and $L\approx2.8\,\rm{fm}$,
and obtained the $\Delta$ resonance parameters $m_\Delta= 1378(11)\,\rm{MeV}$ and $g_{\Delta-N\pi} = 23.8(2.8)$. We have now additionally computed the three-point functions for six source-sink separations ranging from $t_{\rm sep}=0.7 - 1.2\,\rm{fm}$. Here, we present a first look at the three-point functions data by extracting the $N\to\Delta$ transition form factors using the single-hadron approach.