You can't really predict the exact time. Did you book with Amtrak as a group? If so perhaps Amtrak can arrange for a block of seats in one coach to be set aside for your group. In general, I would tell everyone in your group to be at the station 1 hour before the train departs. This should be stated in non-negotiable terms. There is always one person in every group that does not move as quickly, or is inconsiderate, or something which causes the whole group to be delayed. You want to be sure that such a person does not put the entire group at risk for missing the train.
Amtrak usually starts boarding about a half hour before depature with sleeper passengrs and red cap assitance passengers. Then the pre-boards, and sometimes about 10 minutes before departure, the rest of the coach passengers. This is about the latest that boarding occurs. I could be a bit earlier, hence the advice to be at the station early.
Remember that 5, 3, 21, and 7 all leave in about a 2 hour time period so the station will be very busy and confusing to first time Amtrak travelers. Good luck.