The process for a lead FI to create FATCA IDs for its member FIs is relatively quick once the necessary steps are completed. According to the information provided, the lead FI must first create its own FATCA account and complete Part 1 of the registration. After this, the lead FI proceeds to Part 2 of the registration, where it adds the member FIs' information.
Specifically, in Part 2, question 12 of the online registration, the lead FI inputs the required details for each member FI. As soon as the information for a member FI is completed and the "add another" button is clicked, the system generates a FATCA ID and a temporary access code for that member FI. This means that the creation of the FATCA ID for each member FI happens immediately upon the completion of their information and the submission of the form.
Therefore, the time it takes for a lead FI to create FATCA IDs for its member FIs is essentially instantaneous once the member FI's information is entered and submitted in the online registration system.
Sources:
Instructions for Form 8957 (06/2018)
Publication 5118 (07/2021)