What is a good process for developing a new course from scratch?

I strongly recommend backwards design as a way to plan and build a course. The key idea is to start out by clearly laying out for yourself what results (skills, concepts) students in the course should end up with, then figuring out the assessments that will assess this, and then course activities, assignments, etc., that will feed into this. This works very well, in contrast to the "standard" approach of focusing first on content -- making a bunch of readings, slides, etc. -- and then asking later what sort of tests one can make, which invariably leads to the realization that the assessment gets at peculiarities of that particular content rather than the goals you really wanted. With backwards design, things make much more sense. There are a lot of good references on backwards design (just google it), e.g. this.

Assuming you have everything that's supposed to be in the course proposal, and in sufficient detail, I'd first try to select a textbook if this is an undergraduate course. Maybe it's already in the recommended readings, or, if a graduate course, maybe all you need is the recommended readings. If the course proposal needs more detail, flesh it out.

Set a schedule with granularity of at least weekly for instructional topics. (I write a schedule that has the topics, assessments, and reading assignments for each class meeting.)

With the topics set, you can develop the assignments/projects and set a schedule for them that follows and slightly lags the instructional topics.

Write at least a draft of at least the major exams. You need exams and projects so that you can set dates and announce them in the syllabus on the first day of classes. You should also probably determine how many short assessments, i.e. quizzes you will have and set dates for them. Be careful not to over-extend yourself with quizzes. For a 15-week term, I generally have about seven quizzes and six or seven assignments/projects. If that seems like too few, consider that the biggest complaint I get from students is that the workload is too heavy.

Depending on the other demands on your time, you can probably prepare the slides/notes a week or so in advance of the time you will need them. (Don't wait until the night before; that's when emergencies rear their ugly heads.) Don't forget to set aside time for grading.

Revise each assignment, project, and assessment just before it is released to the students to be sure the required material has actually been covered.

This will be a lot of fun if you don't overload yourself during the term. Enjoy!