I try to answer your question but doubt at the same time if what I say would be the answer you expect. Islam means submitting to one and only one God, a one that is not followed or accompanied by a second. He is the Creator, the Owner, the Leader and the Target. He has introduced Himself to His creatures, humans, from the very first day that He Made them, note that our father himself was a prophet of God, so that humans will not be lost in this tangled world of "intellect vs. desire". Then after every time that a society was going wrong He sent another prophet to remind them of the truth. All people in history were expected to be submitted to God, as He is the Needless and Wise and if he commands something the humans themselves would benefit. In this regard, Islam is not a new religion, it only came to complete all those previous versions of the one heavenly religion, so that when it came to completeness the name came to be "Islam", meaning the complete submission to Allah. Also the rules have experienced minor changes and the final rules were in preparation, but the rules of Islam would not be substituted ever after as Islam is the last religion, and when there is no other rule to be added or changed there would also be no prophet after the last prophet, the holiness Muhammad --peace be upon him--.
However, if someone asks you why you believe in Jesus --peace be upon him-- or why Jews believe in Moses --peace be upon him-- you and them would probably answer because Jesus and Moses have proved their prophecy (neglecting what Christians say about the incarnation of God in Jesus) through many miracles, we approve that, but if again you are asked how can you get assured that the miracles have actually happened what would be your answer? You have not seen them happening! You have trusted your parents and other persons to whom you can trust, they don't lie, also you have sensed faith in God and these trustworthy people were the only ones on around who were talking about what you have personally sensed, so that you could now believe in Christianity, everything that they say as there is no other alternatives. However, Islam is only different in one point. Its prophet's miracle is still in our hands, Quran the book, you can read it like you are just beside its prophet, if there is a believe in Islam that would be acquired through reading this book and then confessing that I understand this book being sent from Allah, so I come to Islam and would be a Muslim. Then if all the people on Earth come to you and try to make you doubt in everything you have your belief structure based on a firm ground, it would not shake until you choose the otherwise.
We can guide people to different verses of Quran or Ahadith for them to get familiar with Islam, but making them to believe is only put aside for Allah Himself, as he has warned us we cannot touch anyone's hearth unless He wants them to be touched. The hearths are the territory of Allah only:
It is not required of thee [or more accurately if I am right, up to you] (O Messenger), to set them on the right
path, but Allah sets on the right path whom He pleaseth. Whatever of
good ye give benefits your own souls, and ye shall only do so seeking
the "Face" of Allah. Whatever good ye give, shall be rendered back to
you, and ye shall not Be dealt with unjustly. [2:272]
And (moreover) He hath put affection between their hearts: not if thou
hadst spent all that is in the earth, couldst thou have produced that
affection, but Allah hath done it: for He is Exalted in might, Wise.
[8:63]
Why should ye be divided into two parties about the Hypocrites? Allah
hath upset them for their (evil) deeds. Would ye guide those whom
Allah hath thrown out of the Way? For those whom Allah hath thrown out
of the Way, never shalt thou find the Way. [4:88]
And also see that in many other verses including these ones:
Allah hath set a seal on their hearts and on their hearing, and on
their eyes is a veil; great is the penalty they (incur) [2:7]
"Our Lord!" (they say), "Let not our hearts deviate now after Thou
hast guided us, but grant us mercy from Thine own Presence; for Thou
art the Grantor of bounties without measure. [3:8]
O Messenger! let not those grieve thee, who race each other into
unbelief: (whether it be) among those who say "We believe" with their
lips but whose hearts have no faith; or it be among the Jews,- men who
will listen to any lie,- will listen even to others who have never so
much as come to thee. They change the words from their (right) times
and places: they say, "If ye are given this, take it, but if not,
beware!" If any one's trial is intended by Allah, thou hast no
authority in the least for him against Allah. For such - it is not
Allah's will to purify their hearts. For them there is disgrace in
this world, and in the Hereafter a heavy punishment. [5:41]
Such were the towns whose story We (thus) relate unto thee: There came
indeed to them their messengers with clear (signs): But they would not
believe what they had rejected before. Thus doth Allah seal up the
hearts of those who reject faith. [7:101]
Therefore, according to Quran even our own believing in God is not up to ourselves, there is no guarantee for us to remain believers till our death time, so we should care about it for Allah not to take his giving back:
Even if We did send unto them angels, and the dead did speak unto
them, and We gathered together all things before their very eyes, they
are not the ones to believe, unless it is in Allah's plan. But most of
them ignore (the truth). [6:111]
And last I should mention you a point. There is a specific age in Islam since when the humans are charged for their wrong doings, 9 for girls and 15 for boys. Note that even in Islamic cultures people are not all the same, differences exist between different Islamic cultures, be it Shia or Sunni, be it Iran or Saudi Arabia or Malaysia, and even there are differences between different inside a single Islamic culture. Allah has given a time to every child during which he can learn, first from their parents, then from their friends in schools and also from tutors, then they further and farther enter the society and can learn even more, then it is time to choose their own way and style. Today children are almost playing all their sub-9 and sub-15 ages, but this is not what is expected from them and even their parents. The time Allah has given each individual person to choose his life style and indeed, belief style, is somewhat vital but not the only opportunity for him. Since Quran has stated humans can still be guided easily until they are 40:
We have enjoined on man kindness to his parents: In pain did his
mother bear him, and in pain did she give him birth. The carrying of
the (child) to his weaning is (a period of) thirty months. At length,
when he reaches the age of full strength and attains forty years, he
says, "O my Lord! Grant me that I may be grateful for Thy favour which
Thou has bestowed upon me, and upon both my parents, and that I may
work righteousness such as Thou mayest approve; and be gracious to me
in my issue. Truly have I turned to Thee and truly do I bow (to Thee)
in Islam." [46:15]
And according to Shi'ite Ahadith 40 is the age that if someone is not guided before that then there would be a very small chance that he/she will ever submit to Allah then after, maybe because he/she has generated answers (even if fake and not true) to the very important questions that would make a base for all of his/her beliefs.
Anyway, let me sum up my answer, Guiding in hearth is not something that any of us, even the prophet himself, peace be upon him, can do. We can only guide people to hear the words of Allah and He Himself would show them his signs so that they will know them, then they may accept it or not:
And to rehearse the Qur'an: and if any accept guidance, they do it for
the good of their own souls, and if any stray, say: "I am only a
Warner". [27:92]
And say: "Praise be to Allah, Who will soon show you His Signs, so
that ye shall know them"; and thy Lord is not unmindful of all that ye
do. [27:93]
EDIT.
But beside what we can do there should be a sentence that says "also we must do what we can!" So if we are not doing as much as we can we would be questioned with no doubt. Maybe this website is a place to do this then! If we cannot guide anyone in hearth but we can show them the truth for themselves to decide to come and stay or to leave and stray.