Tl;dr - you are all new to the company, so say that you want to achieve uniformity of reviews & review some of your code, as a group.
Reminiscing; I once had to introduce software engineering to a company that had only previously done one & two person projects. Then they landed "the big one".
I introduced everything. Explained why we needed documentation & what kind, created document templates & document numbering system. Explained requirements & requirements tracing; set up some kind of a coding standard; got everyone to standardize on the same development tools; why we needed testing; why it ought to be automated; how to test; yadda yadda yadda; explained reviewing.
And I ate my own dogfood all the way.
The first design doc, test spec and first piece of code that were reviewed were mine. I had some trouble, but got them to understand that they were not reviewing the person. We were all going to be reviewed, and there were going to be improvements suggested.
For writing a design document, I told them that I was just the secretary. We had had a series of meetings; I had taken notes, and turned "our design" into a document. Did we miss anything? The document was only "mine" briefly; after the review the document belonged to all reviewers, and all were responsible for any problems with it.
For the code review, I had been “the coder” only inasmuch as I had turned “our” design document into code. Did I make any mistakes in transcription? Could I have done it more elegantly, handled errors better, etc? I won’t take comments personally, as we are all trying to make a product together. But, code review, like all reviews, is a responsibility, and after this review, it is no longer “my” code, but “our” code, and when the test team find the inevitable problems, we all share the responsibility.
This all took place in Asia, where the culture does not invite criticism, and certainly not of those above on in the pecking order. Which is why we tore my stuff apart. I and my (western) partner both pointed out a few things, to break the ice, and my explanation that the group owned the review item, not an individual, got them on board. This ought not to be necessary in the West, but often is.
It sounds like your guys don’t need quite that level of explanation, but you might be able to tease something from it.
And you can always just read my Tl;dr ;-)