It depends...
If you set up check-in instructions (which you can only do from the app, not desktop) and the guest uses that, it will send you a notification. (To set that up, go to the Airbnb app, then "listings", select your listing, then scroll down to "Check-in instructions". You can add pictures and descriptions. Then just tell your guests to hit the "key" at the bottom of your conversation to start self check-in)
If you don't have self check-in set up, you'll either need to ask the guest to message you when they arrive (still not reliable) or have another solution like @Ana1136 suggested, whether it's a smart door sensor, smart door lock, or security camera. I have a Ring doorbell that does a good job of keeping an eye on things.