What is your suggestion?
When starting up the engines of an aircraft, they are almost always done asynchronously. For example, engine #2 is often started first and once its fully running, then engine #1 is started. My suggestion is to have this asynchronous engine start-up be reflected in-game, especially for turboprops where there is a clear visual difference.
How would it work in the game?
When pushback clearance is given, the #2 engine is started and is allowed to reach idle thrust before engine #1 is started and then the aircraft pushes back / starts taxi. For turbofan aircraft, a similar process can be followed for the fan. For four-engined aircraft engines #3 and #4 start before engines #1 and #2
Why is this a good idea?
Would enhance realism.
Optional: Image or reference
Here’s examples of engine start-up sequences (DH8D, AT75, B744)