Tongue pulls back slightly from the T position, blending into R. Sounds close to 'chr'.

Americans pronounce true as TROO (/tru/). In "true", the "tr" cluster blends into a "chr" sound — a natural American English pronunciation. This is called the TR Sounds Like CHR, and it's one of the defining features of casual American English. It comes out as TROO. You'll hear it in sentences like "Is the answer true or false?" or "Do you have proof that this news is true?" — more examples below.
Record yourself saying "true" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 3 sounds. Explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the T position, blending into R. Sounds close to 'chr'.

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.
Round your lips into a tight circle. Let your tongue rest in the middle of your mouth, slightly raised.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "true", the "tr" cluster blends into a "chr" sound — a natural American English pronunciation. /t/ shifts toward /tʃ/ ("ch"), so TR sounds like "chr".