Context . The detection and characterisation of planets younger than ~100 Myr offer the opportunity to get snapshots of systems immediately after their formation, where the main evolutionary processes that sculpt mature planetary systems are still ongoing. Known infant exoplanets are currently scarce, and dedicated surveys are required to increase their number. Aims . We aim to determine the fundamental properties of the ~35 Myr old star TOI-837 and its close-in Saturn-sized planet, and to investigate the system’s formation and evolutionary history. Methods . We analysed TESS photometry and HARPS spectroscopic data, measured stellar and planetary parameters, and characterised the stellar activity. We performed population synthesis simulations to track the formation history of TOI-837 b, and to reconstruct its possible internal structure. We investigated the planetary atmospheric evolution through photo-evaporation, and quantified the prospects for atmospheric characterisation with JWST. Results . TOI-837 b has similar radius, mass, and bulk density to those of Saturn ( r b =9.71 −0.60 +0.93 R ⊕ , m b =116 −18 +17 M ⊕ , and ρ b =0.68 −0.18 +0.20 g cm −3 ) and is on a primordial circular orbit. Population synthesis and early migration simulations suggest that the planet could have originally formed between 2 and 4 au, and have either a large and massive core, or a smaller Saturn-like core, depending on the opacity of the protoplanetary gas and on the growth rate of the core. We find that photo-evaporation produced negligible effects even at early ages (3–10 Myr). Transmission spectroscopy with JWST is very promising, and is expected to provide constraints on atmospheric metallicity and the abundances of H 2 O, CO 2 , and CH 4 molecules, and to probe the presence of refractory elements. Conclusions . TOI-837 offers valuable prospects for follow-up observations, which are needed for a thorough characterisation. JWST will help to better constrain the formation and evolution history of the system, and to clarify whether or not TOI-837 b is a Saturn-analogue.