Perhaps at the outset it should be noted that the Amish descended from one of the two main leaders within the Swiss Brethren Anabaptists (soon after called Mennonites) in the 1690s, named Jakob Ammann, who, along with his supporters, eventually split from that body. Most accounts have portrayed Ammann as an abrupt and unyielding leader who demanded a demonstrably pure lifestyle by church members to the point of insisting on applying the "ban" to them when they failed in that regard. This was also known as "social shunning" (based on a scriptural passage) and was viewed as too judgmental by the opposing group within the fellowship.
Consequently, the Amish group withdrew, even being called Amish-Mennonites since they still adhered to the general Mennonite doctrines and continued on their own course even after Ammann died, most of whom emigrated to Pennsylvania, USA, initially in the early 1700s, while yet others from the Alsace-Lorraine area in the mid-1800s emigrated to Southwestern Ontario, Canada, this latter group being my own ancestors. But as it was mentioned in the question above, to this point in time, the Amish would not have stood out nearly as much from the culture surrounding them as they do now because technology wasn't so much the vehicle of their expression of being faithful to their doctrines and to the mindset of their former leader. Surely, their social isolation would have been noted, but as my father told me, it wasn't until the turn of the 20th-century when the automobile and electricity emerged that they then began to make a conscious decision to reject those as being a corrupting influence leading them into unfaithfulness and "worldliness," as my late mother would refer to when informing me about how it was explained to her.
Now, I must say that my direct ancestors did not stay with the Amish who withdrew to an even greater extent in the early 1900s but instead joined with the larger Mennonite body who did not associate technological progress directly with unfaithfulness. And so, it appears that it was during that first decade of the 1900s when the Amish really became earnest about ostensibly "freezing" their lifestyle.