Am I supposed to run the page like campaign at the same time as the boosted posts?

Yes, on day one, create the like campaign and the engagement campaign. They should run at the same time. To clarify the terminology, boosting a post is done directly from within the Facebook page and is not associated with the business manager or ad account. When you create an engagement campaign within the ad account, it is different from boosting a post. So, on day one, you create the page like campaign and the engagement campaign within the ad account, and they run simultaneously. 

For more insight into creating campaigns, refer to the program video Module 1-8 How To Create a Like Campaign. 

Also, don't forget to register for our weekly live Group Mentorship sessions. They are key for getting extra help and deepening your understanding of the program. You will automatically receive weekly invite emails on Tuesday of each week with email subject lines that always begin with "[AdV] - REGISTER" where you can register for each week's calls.