The Euclid Space Telescope will image about 14 000 deg2 of the extragalactic sky at visible and near-infrared wavelengths, providing a dataset of unprecedented size and richness that will facilitate a multitude of studies into the evolution of galaxies. Although spectroscopy will also be available for some of the galaxies, in the vast majority of cases the main source of information will come from broadband images and data products thereof (i.e. photometry). Therefore, there is a pressing need to identify or develop scalable yet reliable methodologies to estimate the redshift and physical properties of galaxies using broadband photometry from Euclid. Optionally, such methods could also include ground-based optical photometry. To address this need, we present a novel method developed as part of a 'data challenge' within the Euclid Collaboration to estimate the redshift, stellar mass, star-formation rate, specific star-formation rate, E(B ‑ V), and age of galaxies using mock Euclid and ground-based photometry. The main novelty of our property-estimation pipeline is its use of the CatBoost implementation of gradient-boosted regression-trees together with chained regression and an intelligent, automatic optimisation of the training data. The pipeline also includes a computationally efficient method to estimate prediction uncertainties, and, in the absence of ground-truth labels, it provides accurate predictions for metrics of model performance up to z ~ 2. We applied our pipeline to several datasets consisting of mock Euclid broadband photometry and mock ground-based ugriz photometry, with the objective of evaluating the performance of our methodology for estimating the redshift and physical properties of galaxies detected in the Euclid Wide Survey. The statistical metrics of prediction residuals vary depending on which mock catalogue and filters are tested. Nonetheless, the quality of our photometric redshift and physical property estimates are highly competitive overall, validating our modelling approach. However, at z ≳ 3.5, the relative sparsity of galaxies resulted in unreliable redshift and physical property estimates, which we argue could be mitigated by building catalogues with better sampling of z ≳ 3.5 galaxies or by switching to the use of spectral energy distribution fitting in this regime. We also find that the inclusion of ground-based optical photometry significantly improves the quality of the property estimation, highlighting the importance of combining Euclid data with ancillary ground-based data from such surveys as the Vera C. Rubin Observatory Legacy Survey of Space and Time and UNIONS.