In the new era of time-domain surveys, Type Ia supernovae are being caught sooner after explosion, which has exposed significant variation in their early light curves. Two driving factors for early-time evolution are the distribution of 56Ni in the ejecta and the presence of flux excesses of various causes. We perform an analysis of the largest young SN Ia sample to date. We compare 115 SN Ia light curves from the Zwicky Transient Facility to the TURTLS model grid containing light curves of Chandrasekhar mass explosions with a range of 56Ni masses, 56Ni distributions, and explosion energies. We find that the majority of our observed light curves are well reproduced by Chandrasekhar mass explosion models with a preference for highly extended 56Ni distributions. We identify six SNe Ia with an early-time flux excess in our gr-band data (four ‘blue’ and two ‘red’ flux excesses). We find an intrinsic rate of 18 ± 11 per cent of early flux excesses in SNe Ia at z < 0.07, based on three detected flux excesses out of 30 (10 per cent) observed SNe Ia with a simulated efficiency of 57 per cent. This is comparable to rates of flux excesses in the literature but also accounts for detection efficiencies. Two of these events are mostly consistent with circumstellar material interaction, while the other four have longer lifetimes in agreement with companion interaction and 56Ni-clump models. We find a higher frequency of flux excesses in 91T/99aa-like events (44 ± 13 per cent).