Yes, you can use a Thunderbolt dock and/or Thunderbolt 2->3 adapter to get what you’re after (note: since you have a Thunderbolt monitor, you *can’t* use a plain old USB-C dock/adapter to do the trick).
Specifically, I’ve done something similar using a CalDigit TS3 Plus Thunderbolt dock on my desk (they’re not cheap though, but I wanted a full dock with all the extra ports and a single cable to my M1, not just an adapter).
In order to make it work, the hookup looks like this:
MacBook M1 -> CalDigit TS3 Plus Dock (via included Thunderbolt cable) -> Apple Thunderbolt 2 to 3 adapter -> Apple Thunderbolt/Cinema Display
In addition to the Thunderbolt dock, you need a Thunderbolt 2 to 3 adapter (Apple makes one) to make everything work as the monitor you have has an old Thunderbolt 2-style connector, whereas the M1 MacBook and the CalDigit Dock support Thunderbolt 3.
If you just want the monitor and no additional ports, then the Thunderbolt 2->3 adapter by itself will do the trick, but you'll also need to power the laptop via its charger, tying up all the ports on the M1. But the Cinema Display has USB and Ethernet ports too so that might be all you need depending on what you want to plug in.