Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Americans pronounce dream as DREEM (/drim/). In "dream", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. This is called the DR Sounds Like JR, and it's why Americans sound more relaxed than the textbook. It comes out as DREEM. You'll hear it in sentences like "I had a strange dream last night".
Record yourself saying "dream" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 sounds. Explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

Press your lips together. Air flows through your nose. Vocal cords vibrate.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "dream", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. /d/ shifts toward /dʒ/ ("j"), so DR sounds like "jr".