The Euclid Wide Survey (EWS) is predicted to find approximately 170 000 galaxy-galaxy strong lenses from its lifetime observation of 14 000 deg2 of the sky. Detecting this many lenses by visual inspection with professional astronomers and citizen scientists alone is infeasible. As a result, machine learning algorithms, particularly convolutional neural networks (CNNs), have been used as an automated method of detecting strong lenses, and have proven fruitful in finding galaxy-galaxy strong lens candidates, such that the usage of CNNs in lens identification has increased. We identify the major challenge to be the automatic detection of galaxy-galaxy strong lenses while simultaneously maintaining a low false positive rate, thus producing a pure and complete sample of strong lens candidates from Euclid with a limited need for visual inspection. One aim of this research is to have a quantified starting point on the achieved purity and completeness with our current version of CNN-based detection pipelines for the VIS images of EWS. This work is vital in preparing our CNN-based detection pipelines to be able to produce a pure sample of the >100 000 strong gravitational lensing systems widely predicted for Euclid. We select all sources with VIS IE < 23 mag from the Euclid Early Release Observation imaging of the Perseus field. We apply a range of CNN architectures to detect strong lenses in these cutouts. All our networks perform extremely well on simulated data sets and their respective validation sets. However, when applied to real Euclid imaging, the highest lens purity is just ∼11%. Among all our networks, the false positives are typically identifiable by human volunteers as, for example, spiral galaxies, multiple sources, and artifacts, implying that improvements are still possible, perhaps via a second, more interpretable lens selection filtering stage. There is currently no alternative to human classification of CNN-selected lens candidates. Given the expected ∼105 lensing systems in Euclid, this implies 106 objects for human classification, which while very large is not in principle intractable and not without precedent. ★This paper is published on behalf of the Euclid Consortium.