Do you have any pointer on why you believe so firmly in an infinite universe ? Reading books on physics (from mainstream authors like Stephen Hawking or Christian Magnan, or from less conventional books like Julian Barbour's End of Time) I got the impression that the current consensus is that the universe is finite, expanding, but currently finite. There may be no limit of its size if, as it seems now, the expansion rate is growing - but right now it has a finite size.

And from a purely theoretical point of view, infinity doesn't seem very coherent to me. Infinity doesn't well, exist, it's only a limit of a finite process. Saying "the universe is infinite" doesn't mean much. Your reasoning seem like it is, to quote your own word, "assuming an infinity that has not been obtained as the limit of a finite calculation", which is an illegal operation in maths.