Error When Trying to Build Solution Offering on APN

Based on the error messages you're receiving, there are a few things happening here:

First, even though you don't want your solution published on AWS Marketplace, creating solutions still requires AWS Marketplace seller credentials. This is a prerequisite for solution creation, regardless of whether you intend to publish it publicly or use it solely for customer engagements.

The registration error you're encountering - "Registration is taking longer than expected" - suggests that your seller registration process may be experiencing delays or issues. Here are the steps you should take:

1. Contact AWS Marketplace Seller Operations Team: Since the error message specifically directs you to contact them, this is your best path forward. They can investigate why your registration is taking longer than expected and help resolve any backend issues.

2. Wait for Profile Approval: If you recently initiated registration, your public profile may still be under review. This review process typically takes two to three business days. During this time, you won't be able to complete certain aspects of seller registration. You should receive an email to your root email address once your profile is approved.

3. If the Issue Persists: If you still can't complete registration after three business days, definitely reach out to the AWS Marketplace Seller Operations team for assistance.

Once your seller registration is complete, you'll be able to create solutions in AWS Partner Central. Remember that for launching opportunities and requesting private offers for customer engagement, you'll also need to be an AWS Partner Network (APN) partner eligible for APN Customer Engagements (ACE).
Sources
Troubleshooting - AWS Marketplace
Multi-product solutions FAQ - AWS Marketplace

I supported a partner through this exact issue. Go to your Create your Profile and Complete Partner Seller Settings (you will find this under Get Started on co-selling) and make sure that it is complete. For my partner, the complete registration with Marketplace was not done and the button to do that was seen only when this was checked. This was necessary before a solution offering was possible.