All official Toggl Track apps (web, desktop and mobile) have two modes for entering time:
Timer mode where you start and stop the timer.
Manual mode where you input time for an activity that already happened.
In the Desktop apps, you can switch between the two modes by hitting ⌘ + D / CTRL + D on the keyboard or by going to:
Toggl Track (in the main menu) -> Switch Mode on macOS.
Cogwheel icon -> Use manual mode on Windows.
If you're unable to start the timer and are stuck with only being able to add duration, hit ⌘ + D or CTRL + D and you'll go back to the normal/timer mode.