Wanikani uses SRS. The wait time is part of the learning. The idea is to stimulate your memory after a period of time. If it is stimulated right away the learning advantage is not that great. @hannah218 has posted links to how the SRS works. I encourage you to read this information because you need it to make the best out out Wanikani.
The delays seems long at the beginning because you still have not had lessons for a lot of items. This will not last. As you get more lessons the review workload will augment considerably. Be patient.
If after learning all this you are still hungry for more studying you can use scripts. They are third party add-ons that augments the features available on Wanikani. The scripts most suitable for extra studying are Self Study Quiz and Item Inspector. You may check them out and try them. Installation instructions are available at the links. Scripts will not accelerate the delay between Wanikani reviews but they will keep you busy while you wait. Disclosure: I am the author of Item Inspector.