In toystory 4, a kid build a toy with trash he found. Some minutes after, the trash pile is alive. The other toys are stunned to see that trash can become a living toy, and even the trash toy wants to die and go to the bin as it thinks it is a trash

In toystory 2, one buzz in supermarket is alive when the main buzz try to steal his belt. Also, buzzes seem to never remember that they are toys, and think they are true space ranger in mission.

They probably gain consciousness once they are manufactured and considered as a toy by someone, with maybe a premade personality human supposed it could have