Understanding How FIFO Exclusive Access to a Single Stream

I am currently creating a music playback application on C#.
I'm looking for a Stream (or equivalent) that meets the following requirements, but I can't find it.

·You can write a byte array at the end of a single stream and read it from the beginning at the same time.

Create write and read threads and
In the writing thread, a music file divided into about 5 seconds is acquired from a web by an Http request and sequentially written in a stream as a byte array.
In order to realize streaming reproduction (while writing the music file to the stream), a byte array on the stream is read and reproduced from the head by a reading thread.

I want to realize these requirements, but they don't work very well.
MemoryStream does not provide FIFO or exclusive access.
If it's Queue, I can't help but get a cut when playing it.

Even if it is not a standard library, it would be fine if it could be implemented in succession.
Thank you for your cooperation.