What birth doesn't God initiate? Yes, if God did not initiate it, it is wrong but I believe God is sovereign and therefore this cannot happen.
If the Bible does not speak to something directly it is our responsibility to find out God's heart on the specific matter. I assume every Christian with the IVF decision in front of them has spent copious amounts of time seeking God's will through prayer, reading the Bible, and in wise counsel as we have since being told in Jan. 2011 that IVF was our only physical chance. Now I 100% believe it is God's will that I do IVF and that if our IVF results in a baby it will be His decision.
God does not need our help to make something happen but yet we understand modern medicine to be a gift. We're not helping God by using medicine, we're utilizing one of His awesome gifts. Again, whatever medical/healthcare decisions we choose or whatever physical resources we us it is God who decides their outcome.
On our end, we must have faith in Jesus and humble ourselves before His throne. We humble ourselves partially by accepting His gifts, salvation, relationship, medicine/healthcare, etc. When we do so e can be assured that His will be done in our lives if we pray so.