The Availability setting determines when the student can submit work:

Do not confuse this with the Allow access settings under Restrict access. The Allow access settings determine whether the student can see the assignment on the course page, or whether the assignment is completely hidden from the student. After the student sees and selects the assignment, the Availability setting determines whether the student can submit work to the teacher.

Note that there is a Due date and a Cut-off date. If you do not enable a Cut-off date, the assignment will stop accepting work on the Due date. If you enable and enter a Cut-off date, the assignment will accept work between the Due date and the Cut-off date. That work will be marked late.

When a student clicks on an assignment, Moodle displays the assignment's description. You usually use the description to tell the student how to complete the assignment. If you enable the setting for Always show description, then if a student enters the assignment at any time, the student will see the description. If you want a student to be able to prepare and work ahead, this is fine. If you disable the setting for Always show description, then if a student enters the assignment before the Allow submissions from date, Moodle will hide the description for the assignment. You might use this feature to prevent students from working ahead.

Assignments that are due soon will appear in the Upcoming events block. If you do not set a Due date, by default, it will be set to today (the day you created the assignment). This will make the assignment show up in the Upcoming events block as if it's overdue. Ensure that you set an appropriate Due date for the assignment.