The epoch when low-mass star-forming galaxies (LMSFGs) form the bulk of their stellar mass is uncertain. While some models predict an early formation, others favor a delayed scenario until later ages of the universe. We present constraints on the star formation histories (SFHs) of a sample of LMSFGs obtained through the analysis of their spectral energy distributions using a novel approach that (1) consistently combines photometric (broadband) and spectroscopic (equivalent widths of emission lines) data, and (2) uses physically motivated SFHs with non-uniform variations of the star formation rate (SFR) as a function of time. The sample includes 31 spectroscopically confirmed LMSFGs (7.3 \textless= logM(*)/M circle dot \textless= 8.0), at 0.3 \textless z(spec) \textless 0.9, in the Extended-Chandra Deep Field-South field. Among them, 24 were selected with photometric stellarmass logM(*)/M circle dot \textless 8.0, 0.3\textless z(phot) \textless 1.0, and m(NB816, AB) \textless 26 mag; the remaining 7 were selected as blue compact dwarfs within the same photometric redshift and magnitude ranges. We also study a secondary sample of 43 more massive spectroscopically confirmed galaxies (8.0 \textless logM(*)/M circle dot \textless= 9.1), selected with the same criteria. The SFRs and stellar masses derived for both samples place our targets on the standard main sequence of star-forming galaxies. The median SFH of LMSFGs at intermediate redshifts appears to form 90% of the median stellar mass inferred for the sample in the similar to 0.5-1.8 Gyr immediately preceding the observation. These results suggest a recent stellar mass assembly for LMSFGs, consistent with the cosmological downsizing trends. We find similar median SFH timescales for the more massive secondary sample.