You can certainly start the claims procedure, but your solicitor will not get a copy of any of the paperwork until such time as the case is closed, which depending on the type of investigation and possible prosecution could take anything between 6 - 18 months.
However, that does not preclude your solicitor from getting the ball rolling and getting off a letter of claim to the person or organisation believed to be responsible for causing the injuries, just don't expect much to happen in the first instance.
Without giving too much away, can I ask what injuries were sustained?