So maybe write the date to a file? If you can be confident that every user will always access the second course from the same computer on which they accessed the first one, you could write a file locally, name it with the title of the first course, and have it contain nothing but the launch date. If not, maybe there’s a shared folder somewhere where everybody can read and write, and you could write a file there; you could either create a single file that lists usernames and launch dates, maybe like this:
and append to it as users launch the course, or create one file per user with a filename like “YourFirstCourseTitle-username.txt” containing nothing but the launch date.
It’s far from secure, but it would work. Fair warning, though: If you have users on different types of devices (PCs, phones, tablets, kiosks …), this would not be an easy lift. If everybody’s on the same type of device, shouldn’t be too bad, really.