Praise be to Allah.
There is no stipulated age for slaughter of any of the an‘aam animals (camels, cattle, sheep and goats), if the purpose is only for food. If someone were to slaughter a lamb that was only one day old or less, it would be permissible for him to eat that meat, because there is no evidence in Islam to indicate that this is not allowed, and because the basic principle concerning what Allah has created for us is that it is permissible. Anyone who says that something is haraam has to provide evidence. Allah, may He be exalted, says (interpretation of the meaning): “He it is Who created for you all that is on earth” [al-Baqarah 2:29].
There are saheeh hadeeths which indicate that the Prophet (blessings and peace of Allah be upon him) ate lamb.
Al-Bukhaari (4101) and Muslim (2039) narrated that Jaabir (may Allah be pleased with him) said: I said: O Messenger of Allah, come with me to my house. Then I said to my wife: I have seen something (i.e. hunger) in face of the Prophet (sa) that caused me concern; do you have anything? She said: I have some barley and a kid (young goat). So she slaughtered the kid and made dough with the barley, and we put the meat in the pot. Then I went to the Prophet (blessings and peace of Allah be upon him) … And he narrated the hadeeth, in which the Prophet (blessings and peace of Allah be upon him) and his Companions ate from that kid (young goat).
According to the hadeeth of Abu Hurayrah, when the Prophet (blessings and peace of Allah be upon him) visited Abu’l-Haytham, along with Abu Bakr, and ‘Umar, Abu’l-Haytham went to make some food for them. The Prophet (blessings and peace of Allah be upon him) said: “Do not slaughter any animal that is producing milk. He said: So he slaughtered a kid (young goat) or lamb for them and brought it to them, and they ate.
Narrated by Muslim (2038); at-Tirmidhi (2369).
The word translated as kid here refers to a female baby goat that has not reached the age of one year.
End quote from an-Nihaayah, Baab al-‘Ayn ma‘a an-Noon.
The scholars, may Allah have mercy on them, have stated that if the foetus of an an‘aam animal comes out of its mother’s womb alive and is slaughtered in the prescribed manner, it is permissible to eat it.
Ibn Qudaamah said in al-Mughni (9/321): If it comes out alive and in a stable condition, and it is possible to slaughter it, but it is not slaughtered before it dies, then it has not been slaughtered properly. Ahmad said: If it comes out alive, then it must be slaughtered properly, because it is another soul.
Ibn Nujaym said in al-Bahr ar-Raa’iq (8/198): If it is known that the sheep was alive at the time of slaughter, it becomes permissible (halaal) by slaughtering, whether it moved or not.
End quote. See also al-Bahr ar-Raa’iq (8/195).
If it is proven that Allah, may He be glorified and exalted, has made it permissible to His slaves to eat that without restricting it to a specific age, then any condition or restriction that is added to that is an innovation in religion and is a transgression against what Allah has prescribed for His slaves.
Allah, may He be exalted, says (interpretation of the meaning): “And say not concerning that which your tongues put forth falsely: ‘This is lawful and this is forbidden,’ so as to invent lies against Allah. Verily, those who invent lies against Allah will never prosper” [an-Nahl 16:116].
And the Prophet (blessings and peace of Allah be upon him) said: “What is the matter with men who stipulate conditions that are not in the Book of Allah? Any condition that is not in the Book of Allah is invalid, even if there are a hundred conditions. What is ordained by Allah and the conditions stipulated by Him are more deserving of being adhered to.”
This hadeeth was narrated by al-Bukhaari (2168) and Muslim (1504).
But if the animal is intended for udhiyah (sacrifice) and the like, then it is essential that it reach a certain age. This has been discussed in detail in the answer to question no. 41899.
And Allah knows best.