"Popping out" is a commonly used phrase that has several synonyms that can be used in different contexts. One such synonym is "emerging," which indicates something or someone is coming out or appearing. Another similar word is "bursting out," which is mostly used when one is suddenly and powerfully leaving or emerging from a place. "Erupting" is also a synonym that can be used for things or people who are coming out suddenly and with great force. Other alternatives include "sprouting," "springing up" and "projecting" which can be used depending on the situation. Overall, choosing the right synonym for "popping out" can significantly change the context of a sentence.