I remember the idea being around when I was a young teenager ( about 50 years ago ). The youth group did a sketch at the Harvest Supper involving a "mobile phone". The handset was represented by something the size of a house brick but the joke was there was another person needed to carry the large battery and antenna. We had no idea how fast the technology would improve.
I didn't get a mobile phone until my youngest son was at school. He had frequent illnesses and as I didn't want to stay at home all the time I got a mobile so I could reassure him that the teacher could contact me to bring him home if he became ill at school. It was a Nokia.