Hi Phillip,
Well, one classical argument is the uncaused cause argument.
Everything
in our world is a cause and effect cascade — anything that happens is
caused by something else earlier in time, which in turn is caused by something
earlier, and so forth, like a string of dominoes but it had to start somewhere.
This leads us to the Uncaused Cause, God. God started the chain of cause
and effect, and only God meets the requirements for the Original Uncaused
Cause.
Related to this is the following.
Ask an atheist
about what caused the Big Bang. Science will tell you that what happened
before the Big Bang is an impenetrable brick wall — Science (well, human
science) cannot get beyond that point. But it's easy to see that God caused
the big bang to occur, even though it's beyond the realm of science to
prove this.
Just demonstrating that there is an absolute scientific truth
beyond the realm of human science to answer is a big win.
Unfortunately, I'm not up on all the arguments, but a good book you may
want to read is the Handbook
of Christian Apologetics by Peter Kreeft and Ronald Tacelli.
Your library may have it, or perhaps you can request it from a library
which does.
Hope this helps,
Eric
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