Is there a way to change the Entry Date? I don't think so.
Actual Start Date? Depending on settings, etc., yes. You can go to the initial task and change its Actual Start date and that will change it on the project.
Are you looking to see all the projects that have been active during a certain time period? I wouldn't use the Entry Date, but either the Planned Start Date or Actual Start date. If you want to include projects in Planning, just make sure you don't filter those out.
BTW, if you copy a project, it does NOT copy over the entry date, the entry date becomes the date that it was copied.
If you're looking to show the number of active projects in a time period, I would filter for those projects that have an actual start date <= the END date of your range, AND an actual completion date >= the BEGINNING of your range. (if you're looking in the future, I'd use the Planned Start Date)