Posting this here in case anyone else runs into the issue, along with a potential solution.
Fresh project just with one dependency,
Following terminal output

λ cargo build
    Updating crates.io index
error: failed to load source for a dependency on `env_logger`

Caused by:
  Unable to update registry `https://github.com/rust-lang/crates.io-index`

Caused by:
  Access is denied. (os error 5)

.cargo in my home folder was marked as hidden in properties under the Attributes section.
Making it unhidden (recursively with subdirectories) seemed to fix the issue.