You're right that the subject () shows his growth.
Here, the subject of the causative verb is . And the object of is . So the subject/agent of "peep out" is .
>
> (≂ **** )
⇒ (=subject) **** (=object) (causative "make something peep out") ( has replaced in your example)
"Sudo makes his growth peep out" → "Sudo shows his growth"
* * *
Some examples of this , "make something peep out", i.e. "show", from :
> * ****
> _He faced the camera with a folded handkerchief **peeping out** of his breast pocket._
> (Literally: (He) made a folded handkerchief peep out of (his) breast pocket, ...)
> * ****
> _The sun **peeped [peeked] out** between the clouds._
> (Literally: The sun made its face peep out... → The sun showed its face...)
>