Though the Bible was nonexistent immediately after Jesus died, and it was decades before all the books we now have were written, the early church was following the teachings of Christ, as taught not only by Jesus to the Apostles, but also passed on by other disciples of Christ.
The idea of only using the Bible as the source of Christ's teachings is not supported by the Bible.
For example, the teachings that were passed on orally were supported here:
2 Thessalonians 2:15 New International Version (NIV) 15 So then,
brothers and sisters, stand firm and hold fast to the teachings[a] we
passed on to you, whether by word of mouth or by letter.
All Scripture does not mean just the Bible, as the Bible wasn't written yet, though some parts were, so this must also mean the oral teachings, which the Roman Catholic Church refers to as Sacred Tradition.
2 Timothy 3:15-17 New International Version (NIV)
15 and how from
infancy you have known the Holy Scriptures, which are able to make you
wise for salvation through faith in Christ Jesus. 16 All Scripture is
God-breathed and is useful for teaching, rebuking, correcting and
training in righteousness, 17 so that the servant of God[a] may be
thoroughly equipped for every good work.
And for more on whether we should follow Sacred Tradition or Sacred Scripture or both:
What is interesting is that the early church had many writings to refer to, many of which we don't include as being inspired, but it is assumed that many people felt they were worth keeping, as they survived over the centuries.
For a good list of these books you can look at http://en.wikipedia.org/wiki/New_Testament_apocrypha.
Also, I don't know if God wants everyone to be Christian, but for all to have a relationship with Him and with others, as He commanded. If we focus more on religion and listen to what our ministers tell us, instead of listening to God and following His commandments, then any miracles they may have done, anything they did to appear righteous is for naught. You can look at 1 Cor 13 and this:
New International Version (NIV)
21 “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom
of heaven, but only the one who does the will of my Father who is in
heaven. 22 Many will say to me on that day, ‘Lord, Lord, did we not
prophesy in your name and in your name drive out demons and in your
name perform many miracles?’ 23 Then I will tell them plainly, ‘I
never knew you. Away from me, you evildoers!’