The biggest issue we usually have re: time for evidence is that students aren’t comfortable with the biggest realization necessary to master this section: that the evidence can be made up! You can draw from personal experience, “a book you read,” “a study you saw,” etc. Many students have a much easier time once they realize that their evidence is JUST there to show support, NOT to show their knowledge of the issue.
If you’re proving the thesis statement that “people are usually happier around friends than by themselves,” you can talk about a recent study showing that the time you spend around people, and not your money, is the key determinant of happiness (I don’t have the specific study, but I’m sure it’s true). Or about your Uncle Ted, who used to be depressed until he started going to weekly meetings with his friends (maybe you don’t have an Uncle Ted, but so what?).
This may feel dishonest, but again, the point is not to prove you know a fact or instance – it’s to use ANY evidence to show that you know how to support a point. Once you emphasize this strategy, I think the issues will go away!