What's the best way to collect all Goodies in Runabout 2?

How do I get items that I have missed once a mission is complete?

For example I found an item box in the Mall on one of my failed attempts, but didn’t get it in my successful attempt. But after finishing the mission I can only access it in Time Trial where item boxes are not a thing?

Do I have to wait until I’ve completed the game at least once?

Something else?