You can use set completeopt=longest
which will insert the longest common text of the matches. (:h 'completeopt'
)
Be sure not to have menu
nor menuone
in 'completeopt'completeopt'
to disable the autocompletion menu.
This way when you'll trigger autocomplete with <C-n>
or <C-p>
you will not have the menu open but the word will be complete with as many letters as possible.