You should only move onto beta if your team feels assured that your timelines, scope and vision are correct according to the money and people you’ve got for this next phase.
Once you’re confident that you want to move to beta, the team should immediately start working on a business case and funding proposal that the department service owner can submit to their organization’s stakeholders for review and approval.
Start these documents early so your team can keep up momentum. It also gives you time to submit the necessary application and service assessment forms and have them reviewed.
If you decide not to proceed to the beta phase, it’s not a failure to stop developing a service after the alpha if your findings show that it’s the best thing to do.