In general, it’s a great idea to start assembly as early as possible – even if 100% of parts have not been delivered yet. Is there a problem with that? I know that “manufacturing” and “assembly” could mean many things in different contexts, but it seems like this would be preferable (if the assembly resources are available) so you don’t have idle labor.
From your question, I assume you are not the one entering the progress? It sounds like you would like to know if assembly starts prior to the completion of all manufacturing steps. Are you familiar with how to set up the custom fields? I might consider setting up a custom duration field which would be actual start minus scheduled start, and if that number is negative then you can have a custom flag or something. Would that work for you?