DS joined Reception able to read fluently.
First reading book had no words.
Second reading book was Level 4 (old ORT).
Next was Level 8.
He was then given everything age appropriate from levels 8 - 14 or so for the first half of Reception, became a free reader with guidance for suitability of each book, choosing from the Year 1/2 and 3/4 classrooms, c. summer term.
I never had to tell them he could read. They assessed him, they read with him, they discovered it, they found out how well he could read, they adapted their planning and his learning to accommodate it (e.g. he was included in daily phonics lessons but the focus for him was on using phonics for encoding rather than decoding).
Yes, I fretted about it initially, got anxious after the first and secid books came home, thought he might get 'stuck' (there was a moment when a TA said he couldn't read 'properly' because he couldn't predict what came next from the pictures 'he keeps turning over the next page' (I pointed out that was to read the words - as a child who is literal minded to a disabling degree he thought that was clearly the best way of finding out what happened next!) but the teacher sorted that out very quickly).
Trust the teacher. Give it a couple of weeks. the ability to read can't be hidden - the teacher will soom notice which child knows what is kept in EVERY drawer because they can read the labels!