Most people got up at dawn and were awakened by the sunlight. Remember that for the majority of human history, the majority of people were farmers living in the countryside and even today this kind of sleep schedule of up at down and asleep by dusk is associated with farmers. But even then this schedule wasnt limited to farmers and applied also to people living in cities with urban jobs. If this sounds strange to you then think about how, in the absence of artificial gas/electric lighting, most people's days would end before sundown regardless because there wouldnt be anything to really do if it was dark. I dont know if you've ever lived through a blackout that lasted into the night but if you dont have access to lightbulbs there really isnt much at all to do once it gets dark other than sleep. Candlelight or torchlight can be used to make sure you dont trip over things but its too dim to allow for the same kind of activity Now yes there would be some people who had specific jobs that required them to rely on dim torch or candlelight such as obvious examples like guards, some servants, people engaged in illegal activities as well as other ones one might not expect like how in Ancient Rome merchants delivering goods on carriages had to do so during the night because of clogged daytime streets and incidents of them running over people. These people probably had some other means of getting up when they were supposed to, probably having someone else wake up them when theyre needed. Speaking of Rome, Episode 88 of the History of Rome podcast has a really good discussion about the average Roman day and how it worked without our concept of regularized time. You see that even while some people like Marcus Aurelius had troubles with overlseeping most people followed the same daily schedule of rising at sunup and sleeping by sundown. Like I said earlier, most people just went to bed if there wasnt something important to be done during the night because there wasnt that much they could do even if they had trouble sleeping.

And when it comes to telling the time of day, well depending the society you lived in there might be something like a church bell or a minaret where people with access to something like a sundial or mechanical clock would announce the current time to the populace of a town or city. And even in non urbanized cultures or locations, you didnt need to be an astronomer to guess what the rough time of day was by just seeing where the sun is or the length of shadows.

I know you're asking about alarm clocks but it seems like the essence of your question has more to do with the regularization of time and how it effected society and with that the more relevant inventions would actually be not only artificial gas/electric lighting (so that indoor lighting no longer relies on the sun) but also the railroad (traveling faster than movement of the sun in the sky means you could no longer rely on grounding time by saying the point where the sun is directly up is noon in a particular location, you needed more regulated time that didnt depend on local factors as much). I'm busy right now but I hope to come back and maybe talk about that some more and provide sources