itch.io has two separate ways to get paid as described on our documentation about getting paid: Direct to you and Collected by itch.io, paid later
As the name might suggest, with Direct to you you collect money directly at time of transaction. We have this available for all accounts, and you can use Stripe Connect and PayPal. When you're configuring your account you can select direct payments on the Payment processors page. Using these systems will make you the merchant of record and put additionally liability on you and your seller account, but also gives you more control over the transactions and funds sent into your account.
Collected by itch.io, paid later is also known as the payouts system. We use our own business accounts to act as merchant of record to sell your game or product, pool the earnings, then pay out to you at a later time. This type of system is a target for fraud so we have to take additional precautions. We will likely never remove the 7 day buffer from purchase to claim (and the additional payout review time), since it enables us to manage risk accordingly. We have been hit with a lot of fraud in the past. For the safety of itch.io we ask that you have some patience when receiving payouts from us. Thanks for understanding.