They knew that Washington would be the first president (if he wanted to be), but didn't really consider what would become of the system once there wasn't any obviously superior candidate available.
The convention held more votes on electing a president than on any other subject.
They were very concerned about the men who were to follow George Washington.
I wrote two squibs on the matter:
Donald Trump: The Echo of our Framers' Uncorrupted President.
http://articlevblog.com/2016/07/donald-trump-the-echo-of-our-framers-uncorrupted-president/
and
http://articlevblog.com/2016/07/the-framers-president/