Context. The William Herschel Telescope Enhanced Area Velocity Explorer (WEAVE) is a new, massively multiplexing spectrograph that allows us to collect about one thousand spectra over a 3 square degree field in one observation. The WEAVE Stellar Population Survey (WEAVE-StePS) in the next 5 years will exploit this new instrument to obtain high-S/N spectra for a magnitude-limited (I-AB = 20.5) sample of similar to 25 000 galaxies at moderate redshifts (z >= 0.3), providing insights into galaxy evolution in this as yet unexplored redshift range. Aims. We aim to test novel techniques for retrieving the key physical parameters of galaxies from WEAVE-StePS spectra using both photometric and spectroscopic (spectral indices) information for a range of noise levels and redshift values. Methods. We simulated similar to 105 000 galaxy spectra assuming star formation histories with an exponentially declining star formation rate, covering a wide range of ages, stellar metallicities, specific star formation rates (sSFRs), and dust extinction values. We considered three redshifts (i.e. z = 0.3, 0.55, and 0.7), covering the redshift range that WEAVE-StePS will observe. We then evaluated the ability of the random forest and K-nearest neighbour algorithms to correctly predict the average age, metallicity, sSFR, dust attenuation, and time since the bulk of formation, assuming no measurement errors. We also checked how much the predictive ability deteriorates for different noise levels, with S/N-I,N-obs = 10, 20, and 30, and at different redshifts. Finally, the retrieved sSFR was used to classify galaxies as part of the blue cloud, green valley, or red sequence. Results. We find that both the random forest and K-nearest neighbour algorithms accurately estimate the mass-weighted ages, u-band-weighted ages, and metallicities with low bias. The dispersion varies from 0.08-0.16 dex for age and 0.11-0.25 dex for metallicity, depending on the redshift and noise level. For dust attenuation, we find a similarly low bias and dispersion. For the sSFR, we find a very good constraining power for star-forming galaxies, log sSFR greater than or similar to -11, where the bias is similar to 0.01 dex and the dispersion is similar to 0.10 dex. However, for more quiescent galaxies, with log sSFR less than or similar to -11, we find a higher bias, ranging from 0.61 to 0.86 dex, and a higher dispersion, similar to 0.4 dex, depending on the noise level and redshift. In general, we find that the random forest algorithm outperforms the K-nearest neighbours. Finally, we find that the classification of galaxies as members of the green valley is successful across the different redshifts and S/Ns. Conclusions. We demonstrate that machine learning algorithms can accurately estimate the physical parameters of simulated galaxies for a WEAVE-StePS-like dataset, even at relatively low S/N-I,N- obs = 10 per & Aring; spectra with available ancillary photometric information. A more traditional approach, Bayesian inference, yields comparable results. The main advantage of using a machine learning algorithm is that, once trained, it requires considerably less time than other methods. C1 [Angthopo, J.; Granett, B. R.; Longhetti, M.; Iovino, A.; Ditrani, F. R.; Haines, C. P.; Morelli, L.] INAF Osservatorio Astron Brera, Via Brera 28, I-20121 Milan, Italy. [La Barbera, F.; Tortora, C.; Spiniello, C.; Busarello, G.; Iodice, E.; Mercurio, A.; Merluzzi, P.; Ragusa, R.] INAF Osservatorio Astron Capodimonte, Via Moiariello 16, I-80131 Naples, Italy. [Fossati, M.; Ditrani, F. R.] Univ Milano Bicocca, Piazza Sci, I-20125 Milan, Italy. [Costantin, L.] INTA CSIC, Ctr Astrobiol CAB, Ctra Ajalvir Km 4, Torrejon De Ardoz 28850, Madrid, Spain. [Zibetti, S.; Gallazzi, A.] INAF Osservatorio Astrofis Arcetri, Largo Enrico Fermi 5, I-50125 Florence, Italy. [Sanchez-Blazquez, P.] Univ Autonoma Madrid, Dept Fis Teor, Madrid 28049, Spain. [Sanchez-Blazquez, P.] Univ Complutense Madrid, Inst Fis Particulas & Cosmos IPARCOS, Madrid 28040, Spain. [Spiniello, C.; Dalton, G.; Jin, S.] Univ Oxford, Dept Phys, Keble Rd, Oxford OX1 3RH, England. [Poggianti, B.; Corsini, E. M.; Gullieuszik, M.; Moretti, A.; Pizzella, A.; Vulcani, B.] INAF Osservatorio Astron Padova, Vicolo Osservatorio 5, I-35122 Padua, Italy. [Vazdekis, A.; Balcells, M.; Ferre-Mateu, A.; Knapen, J. H.] IAC, Inst Astrofis Canarias, Via Lactea S-N, San Cristobal la Laguna 38205, Sc Tenerife, Spain. [Vazdekis, A.; Balcells, M.; Ferre-Mateu, A.; Knapen, J. H.] Univ La Laguna, Dept Astrofis, San Cristobal la Laguna 38206, Sc Tenerife, Spain. [Balcells, M.; Benn, C. R.; Gafton, E.] ING, Isaac Newton Grp Telescopes, La Palma 38700, Sc Tenerife, Spain. [Bardelli, S.; Bolzonella, M.; Cucciati, O.; Pozzetti, L.; Vergani, D.; Talia, M.; Zucca, E.] INAF Osservatorio Astrofis & Sci Spazio, Via P Gobetti 93-3, I-40129 Bologna, Italy. [Bianconi, M.; McGee, S.] Univ Birmingham, Sch Phys & Astron, Birmingham B15 2TT, England. [Cassara, L. P.] INAF IASF Milano, Via Alfonso Corti 12, I-20133 Milan, Italy. [Corsini, E. M.; Ikhsanova, A.; Pizzella, A.] Univ Padua, Dipartimento Fis & Astron G Galilei, Vicolo Osservatorio 3, I-35122 Padua, Italy. [Dalton, G.] Space Sci & Technol Facil Council, RAL, Didcot OX11 0QX, England. [Garcia-Benito, R.; Gonzalez Delgado, R. M.] CSIC, Inst Astrofis Andalucia, POB 3004, Granada 18080, Spain. [Haines, C. P.; Morelli, L.] Univ Atacama, Inst Astron & Ciencias Planetarias INCT, Copayapu 485, Copiapo, Chile. [Jin, S.; Trager, S. C.] Univ Groningen, Kapteyn Astron Inst, Landleven 12, NL-9747 AD Groningen, Netherlands. [Mercurio, A.] Univ Salerno, Dipartimento Fis ER Caianiello, Via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy. [Murphy, D. N. A.] Univ Cambridge, Inst Astron, Madingley Rd, Cambridge CB3 0HA, England. [Talia, M.] Univ Bologna, Dept Phys & Astron, Via Gobetti 93-2, I-40129 Bologna, Italy. C3 Istituto Nazionale Astrofisica (INAF); Istituto Nazionale Astrofisica (INAF); University of Milano-Bicocca; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Centro de Astrobiologia (INTA); Istituto Nazionale Astrofisica (INAF); Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - UAM - Institut de Fisica Teorica (IFT); Complutense University of Madrid; University of Oxford; Istituto Nazionale Astrofisica (INAF); Instituto de Astrofisica de Canarias; Universidad de la Laguna; Isaac Newton Group of Telescopes; Istituto Nazionale Astrofisica (INAF); University of Birmingham; Istituto Nazionale Astrofisica (INAF); University of Padua; UK Research & Innovation (UKRI); Science & Technology Facilities Council (STFC); STFC Rutherford Appleton Laboratory; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Astrofisica de Andalucia (IAA); Universidad de Atacama; University of Groningen; Kapteyn Astronomical Institute; University of Salerno; University of Cambridge; University of Bologna