We investigated the ability of the Euclid telescope to detect galaxy-scale gravitational lenses. To do so, we performed a systematic visual inspection of the 0.7 deg2 Euclid Early Release Observations data towards the Perseus cluster using both the high-resolution IE band and the lower-resolution YE , JE, and HE bands. Each extended source brighter than magnitude 23 in IE was inspected by 41 expert human classifiers. This amounts to 12086 stamps of 10″ × 10″. We found 3 grade A and 13 grade B candidates. We assessed the validity of these 16 candidates by modelling them and checking that they are consistent with a single source lensed by a plausible mass distribution. Five of the candidates pass this check, five others are rejected by the modelling, and six are inconclusive. Extrapolating from the five successfully modelled candidates, we infer that the full 14 000 deg2 of the Euclid Wide Survey should contain 100 000‑30 000+ 70 000 galaxy-galaxy lenses that are both discoverable through visual inspection and have valid lens models. This is consistent with theoretical forecasts of 170 000 discoverable galaxy-galaxy lenses in Euclid. Our five modelled lenses have Einstein radii in the range 0'.'68 < θE < 1″.24, but their Einstein radius distribution is on the higher side when compared to theoretical forecasts. This suggests that our methodology is likely missing small-Einstein-radius systems. Whilst it is implausible to visually inspect the full Euclid dataset, our results corroborate the promise that Euclid will ultimately deliver a sample of around 105 galaxy-scale lenses. ★This paper is published on behalf of the Euclid Consortium.