I agree with Gwen on Marketplace not being critical path for targeting a developer persona early, but yeah, enterprise buyers will want it sooner than later, so I'd do some steps in anticipation of eventually listing:
1. Join the AWS Partner Network
2. Start the FTR (Foundational Technical Review) process
3. Register as a seller on AWS Marketplace (MP)
4. Learn about SaaS billing on MP
Also, just to be clear, you can list Hybrid SaaS on the marketplace, as long as the customer owned data plane in on AWS.
You should be able to kick this off by working with your account team, though you could self-service at least most of it.