It is not necessary or even advisable to wait until OSHA finishes their investigation to gather necessary information related to a work accident case. In fact, you should begin gathering information and speaking with attorneys immediately after the accident!
Building your case is important and needs to be done as soon as possible. If you wait for OSHA to finish their investigation (which can take up to six months), you run the risk of potential witnesses forgetting very important information, video evidence being erased, etc, etc…
If an attorney is willing to take on your case, request that they send a spoliation letter to the employer immediately, and allow your legal team to start collecting evidence and building your case. You can be sure that the employer and their insurance company are already working on their defense, and waiting only puts you at a disadvantage right from the start.