No, you cannot enter time directly from the Projects screen in BQE CORE.
Time can be entered from the Time Entries or Time Card screens under Time & Expenses. When creating a time entry, you can select the relevant project (and phase) from the drop-down list, but the entry itself is not created within the Projects screen. However, you can quickly access the Time Entries screen from within the project using the Links menu. This provides an easy way to navigate and record time entries associated with the selected project. You can also enter time using the Timers module. Check CORE Help Center for details.