For countless kalpas, all living beings have been each other’s parents and dependents. Therefore, it is said that all living beings are my parents. This “I” also refers to all living beings.

Your idea is right and can be confirmed by the Ksitigarbha Sutra. The sutra says that when a Brahmin woman makes offerings to the Tathagata and remembers the King of Enlightened Flowers, not only does her mother "get out of hell, she should be an eternal sinner. They will all enjoy happiness today and they will all be reborn together."

Why is there such a result? What the Brahmin woman did was to save her mother. Why would other people benefit? "The Brahmin girl returned home after finding herself in a dream, and realized this." What truth did she realize? That is: these sinners were all once mothers! Every living being has been our mother, and has been our own mother countless times. That's why I "made a great vow": I hope that in the future kalpas, I will save all sentient beings from sin and suffering and set up expedients to help them liberate themselves.