When you have large numbers of new employees and you can start once a week or every two weeks, you can get managers to start people on the same day. If you run something once a month, you're going to get a lot of resistance especially for those who want someone to start 30 days away from your orientation.

Orientation should definitely occur the moment an employee arrives. That doesn't have to mean, however, that the employee is in a structured, facilitator-led environment from day one. (It should be structured, but it need not all be led by any particular person)

Sounds like it's time to collaborate to find creative compromises so that the employee can be on-the-job with structured orientation activities from the get-go. Training is not the same as orientation and orientation is not the same as indoctrination. Try separating out each activity into those three categories and start brainstorming.

I know several consultants who would be very happy for the business opportunity if you need more specific guidance (this is not self-promotion -- I'm not referring to myself and I have no business interest in their consultancies).