Praise be to Allah, and peace and blessings be upon the Messenger of Allah. To proceed:
What is established regarding the Dajjal is that he has existed since the time of the Prophet, peace and blessings be upon him, and that he is imprisoned on an island, as indicated by the hadith of Tamim Ad-Dari, may Allah be pleased with him, narrated by Muslim. In it, the Dajjal said about himself: “I am the Messiah, and I am close to being given permission to emerge.”
Ibn Kathir and Ibn Hajar mentioned that the hadith of Fatimah bint Qays concerning the story of Tamim Ad-Dari indicates that the Dajjal already existed during the Prophetic era.
As for what is narrated that the Dajjal was born to believing parents and that his mother became angry with him, so he killed her or threw her into the Fire, no authentic report has been established regarding this, and it is not valid to attribute it to the Prophet, peace and blessings be upon him.
A hadith has been narrated concerning this, stating that the Dajjal:
begins by calling people to truth and righteousness, and some people follow him;
then claims prophethood;
then claims divinity;
and great trials appear at his hands, through which he leads astray those who follow him.
However, this hadith does not have an authentic chain of transmission, because its chain contains Sulayman ibn Shihab Al-Absi, whom the hadith scholars judged to be unknown. Al-Bukhari explicitly stated that the chain of transmission of the hadith is not authentic, and Al-Hafiz Ibn Hajar also declared it weak.
Therefore, it is not correct to state with certainty that the Dajjal goes through these three stages based on this hadith.
What is certainly established is that the Dajjal will be a tremendous trial at the end of time, that he will claim divinity, and that he will come to people with extraordinary phenomena and immense trials. The Prophet, peace and blessings be upon him, warned his nation against him with severe warnings.
The Dajjal already existed during the time of the Prophet, peace and blessings be upon him, and this is established in the hadith of Tamim Ad-Dari, may Allah be pleased with him.
It has not been established that he was born to believing parents or that his mother was a believer and then he killed her.
The hadith describing the stages in which he begins by claiming righteousness, then prophethood, and then divinity is weak and not authentic.
What is established is that the Dajjal will emerge at the end of time and claim divinity, and that his trial will be among the greatest trials.
And Allah Almighty knows best.