Hi there.
I’m assuming besides the trial, you otherwise have a monthly subscription. By default PMPro won’t let you have a different period length for the trial and regular billing.
This can be done with our Subscription Delays add on https://www.paidmembershipspro.com/add-ons/subscription-delays/
It will let you set the initial payment to $1, then the monthly payment as you need it, and then you can set the subscription to start in 1 week instead of 1 month.
The Subscription Delays add on requires a paid membership to download from our site. You can find information on how to get it for free from GitHub here: https://www.paidmembershipspro.com/free/