Most postdoc offers come with the condition that the candidate will have a PhD by the time that they start the job. In many cases showing the PhD is part of the initial paperwork.
If you want to start a postdoc with a document saying that all requirements have been met and the degree will be formally conferred at such and such a date, I think the only way to proceed is to ask the institution whether this will be acceptable. I don't think you can predict the answer by looking through the nuances of the job ad.
I was once asked by someone who had accepted a postdoc offer at my university (UGA) whether or not she could start the position with such a document. She came from an institution that only formally conferred degrees once a year. From my perspective, the key point is that I had no idea what the answer was, but I brought it up with my colleagues and the department head, it went further up in the university, and the answer came back: OK, so long as all requirements have been met. (In the end the candidate decided to push harder and actually get the degree awarded in the summer before arrival.)
I have also seen a postdoc -- at a very prestigious American university -- started by someone who had not written her thesis by the time of arrival. The next semester she accepted a second, semester-long postdoctoral position and only around the end of the spring semester did I learn that she was still writing up her thesis. (It worked out fine for her, and today she is a well-known strong person in the field.) The idea of starting a postdoc before completing your thesis is one of those things that would simply never have occurred to me, but apparently it happens. As with most things, having a very influential advisor couldn't hurt.
(My understanding is that in the humanities, it is relatively common for someone to start a tenure-track job without a PhD. They are then given a certain amount of time to complete their PhD while simultaneously navigating all the difficulties of their new job. This practice -- which is almost begging for trouble, in my opinion, and most of the stories I have heard that start this way end badly -- is all but unheard of in mathematics, because there is usually a postdoc done in between. You should probably have a PhD by the time you finish your postdoc!)
Moral: you really need to ask.
Let me end with a remark which leans towards the obvious: nothing is for sure until it happens, but if you have some specific reason to doubt that you'll have a PhD by the start time of a postdoc, you should bring that up ASAP and ideally before you accept the position in the first place. In the current job market, there is no lack of qualified candidates with PhD in hand.