ABSTRACT The variety of star formation histories (SFHs) of z ≳ 6 galaxies provides important insights into early star formation, but has been difficult to systematically quantify. Some observations suggest that many z ∼ 6–9 galaxies are dominated by ≳200 Myr stellar populations, implying significant star formation at z ≳ 9, while others find that most reionization era galaxies are ≲10 Myr, consistent with little z ≳ 9 star formation. Here, we quantify the distribution of ages of UV-bright ($-22.5\lesssim M_{\rm \small UV}\lesssim -21$) galaxies colour-selected to lie at z ≃ 6.6–6.9, an ideal redshift range to systematically study the SFHs of reionization era galaxies with ground-based observatories and Spitzer. We infer galaxy properties with two SED modelling codes and compare results, finding that stellar masses are largely insensitive to the model, but the inferred ages can vary by an order of magnitude. We infer a distribution of ages assuming a simple, parametric SFH model, finding a median age of ∼30–70 Myr depending on SED model. We quantify the fractions of ≤10 and ≥250 Myr galaxies, finding that these systems comprise ∼15–30 per cent and ∼20–25 per cent of the population, respectively. With a flexible SFH model, the shapes of the SFHs are consistent with those implied by the simple model (e.g. young galaxies have rapidly rising SFHs). However, stellar masses can differ significantly, with those of young systems sometimes being more than an order of magnitude larger with the flexible SFH. We quantify the implications of these results for z ≳ 9 stellar mass assembly and discuss improvements expected from JWST.