I used to use TextEdit all the time to jot down quick notes but since the introduction of iCloud it’s insisted on starting=up with a File Open dialog box, on which you have to click the New Document button. A PITA, if ever there was one. Progress, eh?
The following command pasted into Terminal (which is in the Utilities folder within Applications) will make TextEdit open straight to a new document each time, just like the old days. Triple-click the line to select all of it if you can’t see scrollbars and quit TextEdit first if it’s open:
defaults write com.apple.TextEdit NSShowAppCentricOpenPanelInsteadOfUntitledFile -bool false
Should in future you wish to return to the default way of working, paste this in to the Terminal:
defaults delete com.apple.TextEdit NSShowAppCentricOpenPanelInsteadOfUntitledFile