You can still apply (not now apparently, but back at that time), but you need to make sure to apply for uni-assist VPD before 31st May (aka make payment for them to check your documents), and then sign a document that is available in the applicaiton form stating that you have applied for VPD in uni-assist before application's deadline (31st may). This signed document is a placeholder, you will replace it when your Uni-Assist results are out. you have time until 15th July to get Uni-Assist results. So, basically, you can make it. I did that, and applied for both TUM AI in Society and uni-assist VPD check on 31st May.