Use the find command.
Assuming you're using Bash 4.2+, use -printf '%T+ %p\n'
for file timestamp value.
find $DIR -type f -printf '%T+ %p\n' | sort -r | head -n 1 | cut -d' ' -f2
Example:
find ~/Downloads -type f -printf '%T+ %p\n' | sort -r | head -n 1 | cut -d' ' -f2
For a more useful script, see the find-latest script here: https://github.com/l3x/helpers