If you've clicked on a Private Project link and are redirected to the Open Public Portal, one of two scenarios are likely.
NOTE: Before you try any troubleshooting, try highlighting the link as opposed to just clicking on it, then copy and paste it into your browser. If this does not work, please follow the next steps below.
The first thing to check is to see if the project is open yet - review the communication that the Private Link was sent in to ensure that you are not trying to access the opportunity prior to the open date.
The second issue is that the link could have possibly been changed or pasted incorrectly in the communication sent to you. In this case, you'll need to reach out to the Buyer and ask them for a fresh copy of the link.