過ぎる: passing noon and a bag that is too large
Compare time passing noon with excessive size in 大き過ぎる, retaining travel as the stated use against which the bag is assessed.
The square after noon passed
正午を過ぎると広場に人が増えた。 reports the square becoming more crowded once noon had passed. 過ぎる, read すぎる, concerns passing the time reference 正午, followed by the past increase in people.
Passing noon does not provide a count of people in the square. Read the time relation and increase without adding a judgment about lateness or a delayed arrival.
A bag too large for travel
このかばんは旅行用には大き過ぎる。 says that this bag is too large for travel. In 大き過ぎる, the size description 大き combines with 過ぎる to express an excessive degree.
旅行用には supplies the use against which the size is evaluated. Being too large for travel does not establish unsuitability for every use or an instruction to discard the bag.
Passed time and excessive degree
With noon, 過ぎる concerns passing a time point. With 大き, it concerns excessive size. The preceding time or size expression distinguishes the two uses.
No elapsed-time event is stated for the bag, and no bag-size assessment occurs in the noon example. Do not turn both into the same explanation of exceeding a period.
Does the bag's 大き過ぎる for travel describe time passing?
Show the answer and why
No. It assesses the bag as too large for travel. Distinguish that excessive degree from time passing noon with 過ぎる.