Transverse single-spin asymmetries of very forward neutral pions generated in polarized p + p collisions allow us to understand the production mechanism in terms of perturbative and nonperturbative strong interactions. During 2017, the RHICf Collaboration installed an electromagnetic calorimeter in the zero-degree region of the STAR detector at the Relativistic Heavy Ion Collider (RHIC) and measured neutral pions produced at pseudorapidity larger than 6 in polarized p + p collisions at √ s = 510 GeV . The large nonzero asymmetries increasing both in longitudinal momentum fraction x F and transverse momentum p T have been observed at low transverse momentum pT < 1 GeV / c for the first time, at this collision energy. The asymmetries show an approximate xF scaling in the pT region where nonperturbative processes are expected to dominate. A non-negligible contribution from soft processes may be necessary to explain the nonzero neutral pion asymmetries.