How can a human be given free will when he did not choose to come into this life and strive for Paradise or avoid Hellfire, even though Allah is more merciful to His servants than their own mothers?

Allah is not questioned about what He does, but they will be questioned, because He is the Creator of creation and their Owner. Man was created for worship, and Allah is self-sufficient without them. It is not permissible to object to Allah's creation of them for His worship. Allah Almighty enabled man to succeed and triumph, so He sent messengers and revealed books, clarifying for them the path of good and evil, and He did not punish them before sending the messengers. One should not strike parables for Allah, for Allah knows and you do not know. The fact that man is not given a choice in his coming into this world does not mean that he is not given a choice in his actions therein. Allah does not wrong people in the least, and what is obligatory is to submit to what Allah has decreed, and not to exhaust oneself in searching for matters that the mind cannot comprehend.