Hi @Angi_Moore and welcome to the forum. This a great question. The individual projects are NOT created automatically via a form submission. Since forms are part of every Asana project, when someone fills out your form, it will only show up as a new task in the project it is connected to. https://asana.com/guide/help/premium/forms
If your intention is to create a new project, based on you approving a project request (via a form), I would simply create a project called “New Project Request Submissions”. Then in this project, create a form which will be linked to just this project. Then every submission of the form will be populated back into this project as a task.
You can then review and decide on next steps. If you want to proceed with opening a new project, I would recommend to either (1) convert the task submission to a project https://asana.com/guide/help/tasks/actions#gl-convert-to-project or (2) use a template to open up a new project and link the form submission back to the new project https://asana.com/guide/team/advanced/connect-your-work#gl-tasks-multiple-projects
Hope this helps!