Check the FAQs at https://support.google.com/cloud/answer/9110914?hl=en#how-long, if you have any questions. Additionally, if your verification process is taking longer than you had anticipated, I would advise contacting G Suite API Support. If your situation allows it, they might be able to help you hasten the process.
Make sure to check "How do i get my verification completed faster". As a recommendation, send them a video that gives them a tour of your application's functionality and make sure all the information you send when you submit the verification is as precise as possible.
Additional documentation for the Google fit API, I recommend you to review the Authorizing Request documentation.