I tried crating faces but it left missing edges. In the end I was left with all the right lines but there was no vertex in the center.
Here's a follow up image in case you're wondering what I mean. Notice how there's no vertex in the center.
If both sides have the same number of vertices, you can quickly do this by using the Grid Fill tool (CtrlF > Grid Fill) and tweaking the operator settings. A Span and Offset of 2 should do the trick.
It is recommended to use Grid Fill tool (Mesh > Faces > Grid Fill). I would like to give some further tips for it:
With non-corner vertex active:
With corner vertex active: