Why is the Sh’ma a Time-Bound Mitzvah?

In a class I’m taking at my synagogue, we studied the first page of Talmud as part of a broader survey of Jewish thought throughout history. For anyone unfamiliar, the first page of Talmud deals with what time it’s no longer permissible to say the bedtime Sh’ma, with various scholars arguing for different times that it might be “too late” – some say you can say it until midnight, until the end of the first watch, until the sun rises the next morning, and so on.

This got me thinking – why is the Sh’ma a time-bound mitzvah at all? The Torah instructs us to say it “when we get up and when we lie down”, and I would think the most straightforward interpretation is that you say it every time you lay down to sleep, and every time you wake up, no matter what time it is. Just as the brachas before eating are not time-bound, you just say them before you do the relevant action, no matter what time it is.

There’s probably tons of things like this that I’ve just sort of assumed were derived in the Talmud, without ever thinking much about it. But since this is the first page, and already we’re starting from the assumption that Sh’ma is a time-bound mitzvah – where does it come from?