Yes. Lenses can exist with a maximum aperture wider than f/1, and some have been made. A well-known example is the Zeiss Planar 50mm f/0.7, originally developed for NASA and later famously used by Stanley Kubrick to film candlelit scenes in Barry Lyndon.

So from a physics and optical-design standpoint, sub-f/1 lenses are possible. In practical terms, though, they are extremely specialized and difficult to design and use. As apertures get that large, lenses become more complex, expensive, and challenging in areas like size, focus precision, and optical correction. That’s why they are rare rather than impossible.