When you feel that you have finished enough to write it up for submission, do so.
Now you can do a literature search and weave it into your introduction.
Alternatively, submit it; your referees will have much to say about the lit you have ignored.
Get the other folks to do your literature search for you…..
Some, maybe will do your work for you, especially the fresh-out-of-grad-school academics who don’t know any better and the older ones who are actually doing similar research and don’t see their papers cited. But the rest may just send it back with the comment to do a literature search. If the Introduction is thin, and hardly any papers have been cited, chances are the rest of the paper is thin too. If I’m the reviewer, and it appears you don’t have any idea of what has gone before you, I don’t trust your work very much. I just send it back for Major Revisions. Bad enough I get sent papers that are barely readable and get sucked in to English editing. Sometimes I actually do know a few relevant papers the authors haven’t cited, and if the papers looks like they made an effort, I mention a couple because it will help them revise. I’m in the Physical Sciences/Engineering field, so this PoV may not apply to the fluffier side of academia, which may have been the point of the original article, and which I admit I didn’t bother to click on.