We determine the contributions of the rapid (r) and slow (s) neutron capture processes to the Ba isotope mixture, along with Ba, Eu, and Sr NLTE abundances, in a sample of very metal-poor stars. The selected stars formed before the contribution from the main s-process in low- and intermediate-mass stars became significant. Some of our sample stars are enhanced in Sr, with [Sr/Ba] reaching up to 0.7. These stars gained their high Sr abundance from a poorly understood process, sometimes referred to in the literature as a light element primary process, which may appear to be a weak s-process or a weak r-process. Our aim is to uncover the nature of this additional Sr source. The abundances derived from the resonance BaII 4554 and 4934 A lines are influenced by the adopted Ba isotope mixture. We compute Ba isotope mixtures corresponding to different r- to s-process contributions (pure r-process, 80%/20%, 50%/50% and 12%/88%, i. e. solar ratio) and determine the corresponding abundances from the BaII resonance lines in each sample star. Additionally, we determine Ba abundances from weak subordinate BaII lines, which are unaffected by the adopted Ba isotope mixture. We then compare the Ba abundances derived from the subordinate lines with those from the BaII resonance lines. We find a higher s-process contribution to Ba isotopes in stars with greater [Sr/Eu] and [Sr/Ba] overabundances, suggesting that the additional Sr synthesis was due to the early s-process occurring in massive stars. Using Sr-enhanced stars, we estimate the [Sr/Ba] ratio produced by the early s-process and obtain [Sr/Ba]_earlyS_=1.1+/-0.2. The derived value should be regarded as an upper limit, as we cannot definitively exclude the possibility of a contribution to Sr from the weak r-process, which produces Sr but not Ba. Regarding the potential synthesis of Sr and Ba in the i-process in massive stars, our results for Ba isotopes and element abundances argues that there was no detectable contribution from this process within the error bars in our sample stars. In the early Galaxy, before significant main s-process enrichment, barium and strontium were produced primarily by the main r-process and the early s-process, which occurred in rapidly rotating massive stars.