For the first 3-6 months you have to stay in a “Erstaufnahme Einrichtung” and after that time, you no longer need to keep living there. You will then get a permission to look for your own apartment.
Without this permission you can’t apply at the LAF to get your costs covered. Normally the permission is issued automatically and you receive it via post. But it could happen that this does not work. IF it doesn’t work, you can make an appointment with the administration team at LAF to ask when you will receive this permission.
If you have your resident permit and you already receive financial support from the Jobcenter, you can directly apply for the covering of your costs at a jobcenter. The LAF is then not in charge anymore.