The phrase “創業以来ながらに” means “since the founding” or “since the beginning.” In the context of the sentence, “創業以来ながらにして伝統の味を守り続けている” means “Since its founding, it has continued to preserve the traditional taste.” The correct reading for “創業以来” is “そうぎょういらい,” and “ながらに” means “while” or “in the state of.”
うまれ: This means “birth” but does not fit the context of “since the founding.”
はじめ: This means “beginning” and fits the context of “since the founding.”
そざい: This means “creation” but does not fit the context of “since the founding.”
おこり: This means “occurrence” but does not fit the context of “since the founding.”