I know this is closed without likelihood to reopen but I forgot out this most revealing verse on the topic:
Proverbs 25:2 NIV
It is the glory of God to conceal a matter;
to search out a matter is the glory of kings.
I cannot really answer this without it being mostly opinion, but here it goes anyway.
I would say that maybe the Amish think technology is not God's intention. I don't think we will get many Amish on this site, however.
I don't see how anyone who takes the Bible can say anything is not God's intention. There are just too many verses indicating and even straight up saying that nothing happens without God knowing about it and either letting it happen or intervening. So I would say that if there is a Christian sect that actually preaches this, they are likely small and do not fully take the Bible.
I have this picture of those old crotchety men complaining about those darn kids today and their fandanggeled e-lec-tronics. Then they go on to say that God never intended us to do this and that with such and such technology. I have to say that he just must be speaking out of ignorance.
I think it is clear that God very much intends for us to understand His creation and that is all supported in the Creation story in Genesis. The first is that man is made to be like God, who is a creator, and we are charged with ruling over (caring for) the earth and all that is in it.
So God created mankind in his own image,
in the image of God he created them;
male and female he created them.
God blessed them and said to them, “Be fruitful and increase in number; fill the earth and subdue it. Rule over the fish in the sea and the birds in the sky and over every living creature that moves on the ground.” Gen 1:27 NIV
Here it says that man is made in God's image then immediately blesses man and charges him with the care of the entire Earth. Holy Cow! Do you see what just happened here? God gave man some of His own spectacular abilities then gave him all of creation. That sounds like a licence to do. A licence to do like God and create, and build and 'see that it is good'. This sounds to me that no only does the Bible want us to be 'scientists' (which comes from the Latin word for knowledge), and not only encouraged it, but He charged us with it. We are to rule over all of creation as He rules over us. That means we are to know His creation as he knows us, and also care for it and cherish it, and add to it when we can so that 'it is good'.
Later God brings every animal to Adam to name.
Now the Lord God had formed out of the ground all the wild animals and all the birds in the sky. He brought them to the man to see what he would name them; and whatever the man called each living creature, that was its name. So the man gave names to all the livestock, the birds in the sky and all the wild animals. Gen 2:19
This has a lot going on when you include what is before and after, but what is often missed is that naming something has often been the symbol of your authority over it. This is saying that creation is the same a belonging to us as it does to God because He gave it to us. This also shows that God forced Adam to know His creation before it was even complete; before Eve was made. God very clearly wants us to explore and know His creation.
Now as for knowledge that God meant for us to have, I think actually the knowledge is in question is wisdom, at least in full. It was the wisdom gained from eating of the Tree of Knowledge that brought about the fall. The fall did not come because Adam made a scientific discovery. The fall did not come because Adam learned something magnificent about Creation and then applied it in some way. No. The fall came because Adam and even gained spiritual knowledge, or wisdom; they gained knowing what was good and evil. Without this knowledge they could only do good. They were blameless. So if they could only do good then any scientific thing they might have done would also only be good. They would be doing their holy charge: Ruling over the Earth.
Now about technology today. All of that only exists because someone used their God given ability to create like He does. Someone learned something magnificent about Creation, applied it to something specific, then created something good. At least we hope it is good. I am not the type to condemn something simply because it exists, but I think it is clear that knowledge and scientific discovery can lead to nasty inventions. Nuclear weapons are the first that come to mind. The point is that we can create and are meant to do so, and we only have the ability to create evil because of the spiritual wisdom that the Tree of Knowledge gave us. So you see that this spiritual knowledge combined with our ability to create can make us pretty nasty, but if we can be true to God we can also create some awesome things that add to Creation's goodness instead of take away.
So in summary, we were made to be creative like God. For us to be creative like God we must first be intelligent, innovative, exploring, and inventive. Science is the Christian thing to do. Embracing discovery and inventions that glorify God and add to Creation's goodness is the Christian thing to do.