As Ralf said in the comments, there is no built-in command that does this. I would recommend using either ji, jI, or jA for this purpose, since those are all only two keys, and they're fairly normal vim idioms.
If you'd really like to do this with a single keystroke, you could always overwrite the o command to not make a newline. To do this, add one of the following lines to your .vimrc (depending on which behavior you want):
" Enter insert mode at the beginning of the next line
nnoremap o j0i
" Enter insert mode at the end of the next line
nnoremap o jA
" Enter insert mode at the first non-whitespace character
nnoremap o jI
(Note that the lines starting with " are just comments)
Unfortunately, this overwrites o which I think is a very useful command. Normally, to add your own shortcuts without overwriting the default ones, it's standard to use <leader>. However in this case, something like
nnoremap <leader>o ji
would be pretty pointless since it's not any shorter than just manually doing it with ji
jimaybe followed by<C-T>to get the indent. See:help i_CTRL-T. Maybe better:jAin case there are already leading spaces/tab. – Ralf Dec 30 '18 at 18:16