Thanks for writing and your interest. One of the first items of business for the new ASWF will be to create the "project submission process". This will allow new and existing projects to be submitted to the ASWF, allow them to be evaluated to insure they are a fit into the mission and resources, and then accepted into the ASWF. Our conversations to date have been around some critical existing projects for the media business whose maintainers have expressed interest. Projects like OpenEXR, OpenColorIO and OpenVDB have been discussed so far. There are a lot more, but the ASWF will have to evaluate each to make sure the resources to host the community are in place to take on more projects.
To get some background on how the Linux Foundation generally approaches project submissions, you might like reading this presentation by Chris Aniszczyk (https://www.slideshare.net/caniszczyk/bringing-an-open-source-project-to-the-linux-foundation). Each organization under the LF (of which ASWF is one) specifies their own submission process so the ASWF may have some customization, but I think those slides provide some good background.
Hope that help.