We'd recommend filing your change of address form at least 2 weeks prior to your move as it typically takes the USPS between 7-12 business days to process mail forwarding requests.
Once they've finished processing your request, you'll receive a USPS Confirmation Letter in the mail and begin seeing your forwarded mail a few days later.
Please note: It can take up to 10 business days for the USPS to redirect mail from your old address to your new address. If it's been more than 10 business days since receiving your USPS Confirmation Letter, you'll want to contact your local post office (at your old address) for additional assistance!