Make the request as soon as the appointment is scheduled. Some arrangements, an interpreter in particular, need lead time, and a request made days before may not be filled. If the need arises later, contact the office promptly rather than simply not attending.
Do not let the date pass unaddressed
Missing a scheduled appointment can affect the case, and an unexplained absence is harder to resolve than a request made in advance. If the family member cannot attend on the date, ask the office how rescheduling works and follow its instructions. Keep the employer informed about timing in general terms so start dates and travel plans stay adjustable while arrangements are confirmed.
Work backwards from the date rather than forwards from today. Fix the appointment date first, then the day the arrangement has to be confirmed to be usable, then the day the request must be sent to leave room for one round of clarification, and only then the day the travel is booked. Interpreters and specialised equipment are the constraints that move least, so they set the earliest deadline in the chain.
Hypothetical example: a plant pathologist waits until the employer confirms a start date before requesting an interpreter, discovers the lead time runs past the appointment, and now has to choose between attending without the arrangement and asking to move a date the employer has already built a schedule around. Requesting early costs nothing if the appointment later moves; requesting late removes the option entirely, and an absence with no prior contact is the hardest position to recover from.