"晚餐开始的时间" can be translated into English as "the time when dinner starts" or "the starting time for dinner".
Both expressions are commonly used and convey the intended meaning clearly. For example:
What is the time when dinner starts? （晚餐几点开始？）
Could you tell me the starting time for dinner? （你能告诉我晚餐开始的时间吗？）