Yes, it is certainly possible. For example, in Haskell, the Foreign Function Interface provides the necessary functionality for (a) calling low-level routines for accessing hardware, and (b) managing memory explicitly. The GHC runtime system even contains its own ELF loader.

The HaLVM is an example of Haskell running natively without an operating system underneath. It handles the necessary MMU interaction, and has basic device drivers and a network stack implemented in Haskell.

There have been other examples in Haskell: House is a proof-of-concept OS written in Haskell, and it is (or was) possible to write Linux Kernel Modules in Haskell.

In other languages, check out Mirage OS in OCaml, and there have been OSs implemented in ML.