From your description, I picture a small general membership gym which has personal trainers as independent contractors and NOT a personal training studio that only has trainers.
Getting the first paying client is always difficult, and you may need to do some gratuitous training (or very low charge) so that people can actually see you train somebody. It is no chink in your armour to tell people that you are just certified and want to start on somebody to have a reference for future clients. This itself will give you confidence. If you choose to do it, treat the relationship with utmost professionalism. Trust me, other people will be watching you.
An additional way is to strike up a good working relationship with the owner of the gym. Since it allows you to train as an independent trainer, I assume that the owners are present. Can you train their wife, son, daughter?
Whenever you are at the gym, always wear your uniform that identifies you as a trainer. Have business cards on you wherever you go.
The first year is not easy. You will have more downtime than you want. Use it to study, study, study. If I were to observe a trainer with her nose in an anatomy book, I’d take notice.
I saw that LaRue and Joanne hve already answered another question of yours. Please consider my comments as an add-on.
I wish you good luck. You are about to embark on a wonderful journey even though the first few steps may be a little difficult.