First Drill Next Weekend

I recently enlisted in the National Guard. Next weekend is my first drill in RSP (essentially pre-basic training) Well, I'm not horribly out of shape, clearly I'm within the limits of their qualification for enlistment. However... I can't seem to do a single full military style pushup yet. Therefor this week, I'm going to go hard. I don't want to be "that girl" who can't do diddly squat.

Any tips on getting the most put of this week? I do not have gym access or any weights at home right now. I do however have my body, a floor, and a mat