We present the results of a new selection technique to identify powerful ($L_{\rm 500\,MHz} \gt 10^{27}\,\text{WHz}^{-1}$) radio galaxies towards the end of the Epoch of Reionisation. Our method is based on the selection of bright radio sources showing radio spectral curvature at the lowest frequency (${\sim}100\,\text{MHz}$) combined with the traditional faintness in K-band for high-redshift galaxies. This technique is only possible, thanks to the Galactic and Extra-galactic All-sky Murchison Wide-field Array survey which provides us with 20 flux measurements across the 70–$230\,\text{MHz}$ range. For this pilot project, we focus on the GAMA 09 field to demonstrate our technique. We present the results of our follow-up campaign with the Very Large Telescope, Australian Telescope Compact Array, and the Atacama Large Millimetre Array to locate the host galaxy and to determine its redshift. Of our four candidate high-redshift sources, we find two powerful radio galaxies in the $1<z<3$ range, confirm one at $z=5.55$, and present a very tentative $z=10.15$ candidate. Their near-infrared and radio properties show that we are preferentially selecting some of the most radio luminous objects, hosted by massive galaxies very similar to powerful radio galaxies at $1<z<5$. Our new selection and follow-up technique for finding powerful radio galaxies at $z>5.5$ has a high 25–50% success rate.