In these cases of a locked trigger thumb, we typically, eventually perform surgery to release the trigger thumb. It is a surgery that works, has very low risks (i.e., low complication rate), and happy parents and patients.
Less commonly, kids may have a thumb (or finger) that actually pops. This is more like the adult type of trigger digit. In this case, sometimes it hurts and sometimes it does not. This video shows an example of a child who could make her thumb pop. It was essentially stuck in a flexed position but she could, with a notable effort, straighten the thumb. Clearly not painful (but mom reported that sometimes it would be uncomfortable). This shows the mechanical nature of this problem- that is the tendon can't move through the tendon sheath and must be pulled through (with a pop). Check it out.