First of all, congratulations on completing a self-assessment. That's the first step to improving you company, your products, and the satisfaction of your customers.
There is no specific rule against performing a ML3 appraisal "out of the box" without first performing a ML2, although the SEI cautions you that you "should" not skip levels. That said, I've performed a number of appraisals for organizations that started at ML3. So it's possible.
It may not be advisable though. In order to deploy a useful and sustainable process that actually helps your company (a novel idea!) it's helpful to think in terms of releases and iterations. People learn incrementally, as do organizations, and your chances of success are dramatically increased if you deploy smaller components of the process over time.
ML2 is designed to cover the basics of running a project-based organization. It may seem like it's easy, but it can be difficult, and the results can be dramatic. It would be healthy for your organization to first achieve CMMI ML2, run it for a year or two, and then address ML3.
But, that said, I've seen companies push it through, although the results have not all been successful. If you're going to do it, consider conducting a less formal SCAMPI-C or SCAMPI-B appraisal prior to your SCAMPI-A to ensure that you really ARE performing at ML3 before you conduct an appraisal that goes into the public record. Good luck!