We predict feasibility of the photoassociative formation of Sr
2 molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the
c${}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Pi}}_{u}$,
A${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}$, and
B${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}$ states. It creates not only an effective dipole moment allowing free-to-bound transitions near the
1S+3P1 intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited-state levels to deeply bound levels of the ground
X${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{+}$ potential, with ${v}^{\ensuremath{'}\ensuremath{'}}$ as low as ${v}^{\ensuremath{'}\ensuremath{'}}=6$. The spin-orbit interaction is responsible for both optical pathways. Therefore, those excited-state levels that have the largest bound-to-bound transition moments to deeply bound ground-state levels also exhibit a sufficient photoassociation probability, comparable to that of the lowest weakly bound excited-state level previously observed by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)]. Our study paves the way for an efficient photoassociative production of Sr
2 molecules in ground-state levels suitable for experiments testing the electron-to-proton mass ratio.