People would leave messages and call each other back later. This sometimes resulted in “phone tag.”
Before that, there were no answering machines, and you just called and hoped someone was home. Or you’d prearrange a time to call, e.g., “I get home from work at 6, so you can call me any time after that.” Or, “I’ll call you at 10 o’clock on Saturday morning.” It was normal and we were used to it.
I have a mobile phone now, but it’s mainly for Internet and the occasional text. I detest talking on the phone. I make one or two calls a year, to the bank or the government. My ringer is turned off, and I don’t answer the phone or listen to messages; I figure anyone who calls my phone is a telemarketer.
I have a separate number for voicemails only; I give that number out on a need-to-know basis (government, etc.). It might be hours before I am aware that I have a message. This works fine for me.
You might have something else in mind. I just mention what I do to show that it is possible to live without being constantly and instantly available to everyone via phone.