All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Hadeeth means that whomever Allah keeps alive till the age of sixty has no excuse for refraining from repentance and for not devoting himself to Allah, The Almighty, because, by this age, his life is coming to its end and he has already lost the strength of youth, which fuels the inclination to worldly pleasures and pursuit of (sinful) whims.
Commenting on this Hadeeth, Al-Munaawi said: “His saying ‘Allah leaves no excuse for a person’ means that such a person would have no excuse left, such as saying, ‘Had I lived longer, I would have done what I was commanded to do.’ It could also mean that Allah gave him more than enough chance by granting him an ample amount of time to live and reach the age of sixty. The Hadeeth specifies the age of sixty because it is close to the average lifespan (between sixty to seventy years of age, as specified in the relevant Hadeeth). It is also the age when one is often inclined to repentance and returning to Allah, The Exalted, in anticipation of death, being more likely to befall him at that point. A person at that age should keenly seek forgiveness, regularly perform acts of obedience, and wholeheartedly devote himself to worship in preparation for the Hereafter. Moreover, the wording of the Hadeeth cannot be understood the other way around, i.e. that Allah is the one who is to offer excuses for inflicting the punishment upon the slave in such a case, because an excuse is to be presented by the slave of Allah to His Lord. The Hadeeth essentially means that Allah, The Exalted, has left such a person no excuse to present (for his disobedience), and this is the basic rule when speaking about excuses in a context involving a ruling entity and a ruled one.” [End of quote]
Thus, it becomes clear that the Hadeeth does not mean that a person below the age of sixty has an excuse to disbelieve in Allah, The Exalted, or disobey Him; Allah forbids!
As for the excuse of ignorance (regarding disbelief), it is a thorny and complex issue, and scholars discussed it at length. There is no room to cite their discussions in a Fatwa. It is adequate for a Muslim who is competent for religious assignments to know that whoever adheres to any religion other than Islam is considered a disbeliever, and the relevant rulings that apply to non-Muslims with regard to the worldly life apply to him. As for the Hereafter, his fate will be determined by Allah, The Exalted. He is The Wise and Just, and He weighs with an even balance and wrongs none. It is incumbent to believe that Allah, The Exalted, will only torture the ones against whom evidence has been established and who have no excuses for their disbelief, and that none loves to accept the excuses of people more than Allah, The Exalted, as stated in the authentic Sunnah. Ibn Al-Qayyim, may Allaah have mercy upon him, said about the levels of the Muslims competent for religious assignments in his book Tareeq Al-Hijratayn (p. 610): “Allah, The Exalted, will judge between His slaves on the Day of Resurrection according to His wisdom and justice, and He will only torment those against whom the evidence has been established by His Messengers. This is an established fact with regard to all people in general. As for specific individuals and whether or not the evidence has been established against them, this cannot be determined by us and is between Allah and His slaves. Rather, it is incumbent on a Muslim to believe that whoever follows any religion other than Islam is considered a disbeliever and that Allah, The Exalted, will only torment those against whom the evidence has been established by His Messengers, and this is with regard to all people in general. As for specific individuals, their fate is referred to the Knowledge and Wisdom of Allah. This is as far as the reward and punishment in the Hereafter are concerned. As for the rulings pertaining to the worldly life, they are based on the outward appearances. The non-Muslim children and insane individuals, according to the rulings pertaining to the worldly life, are declared disbelievers, and the same rulings that apply to their non-Muslim guardians apply to them. This detailing eliminates the problematic aspect in this regard.” [End of quote]
Whoever wishes to read more about this topic may refer to the aforementioned reference, if he understands Arabic. This is sufficient in this regard; delving deeper into further thorny details would not lead to doing good deeds, and no Muslim is Islamically required to know it.
Allah Knows best.