Although I do know of a few instances where professional or observatory mirrors have been made by alternate materials, it was primarily for targeting specific nuances, like weight reduction and low thermal expansion etc.
I was more keen on finding a material whose primary unique selling point is low cost ;P , keeping in mind a budding amateur astronomer.
Front-surface glass mirrors weren't developed until the 1850s. Before that, the most common material was speculum metal, a high-tin bronze. Notable examples include Isaac Newton's 1668 prototype and William Herschel's late 18th century telescopes. Since speculum metal tarnished easily, it was common to have a spare mirror to continue observations while the other was being reconditioned. Reflectivity and thermal characteristics were not great either.
Good, fast , cheap -- pick any two. And here you need to add things like "machinable," "stable," "nontoxic."
So, there are plenty of metal mirrors but they are much more prone to deformation than a nice rigid glass structure. There are mirrors of SiC (with overcoat, just like glass) for strength and thermal properties. There have been primaries consisting of a tub of liquid Hg, spun at just the right speed to get the desired curvature.
Now, if you're looking to make relatively small primaries for use in non-stressing environments, you could consider carbon-fiber or even 3D-printer resin-based approaches. These methods will produce a good "blank" but will certainly need some final fine polishing to get the surface roughness down under a fraction of a wavelength.
Can a material other than glass be used for making telescope mirrors?
Yes!
From this answer to Why are telescope mirrors made of glass?
They are not always made of glass. In situations where mass counts and thermal variations can be large, optical telescope mirrors are sometimes made out of silicon carbide instead.
From this answer to How are space telescopes stabilised to a perfect standstill?:
Silicon carbide is a very popular material in newer space telescopes and is found in the optical system of too man of them for me to remember, but here is mention of it in GAIA's optical bench answer and in New Horizion's LORRI telescope answer.
above: Gaya's Silicon Carbide Optical Bench, with the two objective mirrors of it's twin telescopes pointing 106.5° apart. From Spaceflight 101, image credit: ESA/Astrium.
above: The LORRI telescope is described for example in the ArXiv preprint Long-Range Reconnaissance Imager on New Horizons
