Implementing wait-free consensus with queues
This paper Some results on the impossibility, universality, and decidability of consensus (by Prasad Jayanti and Sam Toueg, 1992) directly answers your question.

We study how initialization of shared objects affects their ability to solve consensus. In particular, although a queue or a stack can solve name-consensus
between two processes, we prove that an initially empty queue or stack cannot.
However, with a tiny extra resource such as a 1-bit safe register, an empty queue or stack suffices to solve consensus.

Please check Section 5 for impossibility proof and algorithm.

Please also check the paper &quot;On the Importance of Registers for Computability&quot; by Rati Gelashvili, Mohsen Ghaffari, Jerry Li, and Nir Shavit, 2014.
In the second paragraph of Introduction, the authors claim that:

(1) We show that $\ldots$ two queues in arbitrary initial states are sufficient for solving two process consensus.
(2) On the other hand, we prove that it is impossible to solve two process consensus using a single empty queue.

A little conclusion is:

In other words, unless you have multiple queues or multiple registers, a queue’s ability to solve consensus is completely dependent on its initialization.

There are many propositions/lemmas/theorems in this paper. And they are not limited to the queue object. I think it may contain what you want to know (I will read it carefully when I have time).