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The first billion years of cosmic history remains largely unobserved. Wedemonstrate, using a novel machine learning technique, how combining upperlimits on the spatial fluctuations in the 21-cm signal with observations of thesky-averaged 21-cm signal from neutral hydrogen can improve our understandingof this epoch. By jointly analysing data from SARAS3 (redshift $z\approx15-25$)and limits from HERA ($z\approx8$ and $10$), we show that such a synergeticanalysis provides tighter constraints on the astrophysics of galaxies 200million years after the Big Bang than can be achieved with the individual datasets. Although our constraints are weak, this is the first time data from asky-averaged 21-cm experiment and power spectrum experiment have been analysedtogether. In synergy, the two experiments leave only $64.9^{+0.3}_{-0.1}$% ofthe explored broad theoretical parameter space to be consistent with the jointdata set, in comparison to $92.3^{+0.3}_{-0.1}$% for SARAS3 and$79.0^{+0.5}_{-0.2}$% for HERA alone. We use the joint analysis to constrainstar formation efficiency, minimum halo mass for star formation, X-rayluminosity of early emitters and the radio luminosity of early galaxies. Thejoint analysis disfavours at 68% confidence a combination of galaxies withX-ray emission that is $\lesssim 33$ and radio emission that is $\gtrsim 32$times as efficient as present day galaxies. We disfavour at $95$% confidencescenarios in which power spectra are $\geq126$ mK$^{2}$ at $z=25$ and thesky-averaged signals are $\leq-277$ mK.

Joint analysis constraints on the physics of the first galaxies with low frequency radio astronomy data