Hi Aram, in order to get someone into an Engagement Program, there needs to be a smart campaign that inserts them. I'd put the wait step of one week in that smart campaign, so it should look like:
Smart List: criteria that you've used to designate those who are paid search form submissions
Flow: Wait 1 week, then add to engagement program.
You might also want to put something between the wait 1 week and add to engagement program steps that will check that they haven't done something additional that would warrant them not being added to your engagement program.
Hope this helps!