Recovery mode option is not appear

Hope that helped, by the way, this is the article the error refers to, and where you will find the links I posted previously:

If your Mac starts up to an exclamation point in a circle:

https://support.apple.com/HT211868

Best of luck!

1. Make sure that your Mac is up to date. If you're using iTunes, make sure you have the latest version of iTunes. 
2. On a Mac with macOS Catalina, open Finder. On a Mac with macOS Mojave or earlier, or on a PC, open iTunes. If iTunes is already open, close it, then open it again. Find out which macOS your Mac is using.
3. Keep your device connected and wait until the recovery mode screen appears:

• • iPad models that don't have a Home button: Press and quickly release the Volume Up button. Press and quickly release the Volume Down button. Press and hold the Top button until your device begins to restart. Continue holding the Top button until your device goes into recovery mode.
  • iPhone 8 or later: Press and quickly release the Volume Up button. Press and quickly release the Volume Down button. Then, press and hold the Side button until you see the recovery mode screen.
  • iPhone 7, iPhone 7 Plus, and iPod touch (7th generation): Press and hold the Top (or Side) and Volume Down buttons at the same time. Keep holding them until you see the recovery mode screen.
  • iPad with Home button, iPhone 6s or earlier, and iPod touch (6th generation) or earlier: Press and hold both the Home and the Top (or Side) buttons at the same time. Keep holding them until you see the recovery mode screen.

Hey there!

This article may tell you the ways to get to recovery mode, depending on your model of Mac:

How to reinstall macOS:

https://support.apple.com/en-us/HT204904

As said, if using an older Intel chip Mac, the startup commands would involve Command and R, among other combinations.

If using an M1 Mac, holding the power button should bring you to “Loading Startup Options”, then by clicking “Options” and authenticating should take you to the utilities menu. If it doesn’t take you to startup options, then something else is going on.

(However from experience, for whatever reason some newer Macs still respond to Shift Option Command R on startup, don’t ask me why).

Otherwise, can you say the reason for trying to boot to recovery, and the circumstances around it? That may not answer the question, but may help to find a solution. Cheers!

Maybe the factory install is incomplete and you should backup, erase the disk and cleanly re-install Big Sur. Or get a new replacement unit.

https://discussions.apple.com/thread/252988275?answerId=255735989022#255735989022

I see, so you’re trying to access Startup Security Utility:

https://support.apple.com/en-us/HT208198

Well that will make it difficult, perhaps the firmware needs to be revived:

Intel Macs:

https://support.apple.com/guide/apple-configurator-2/revive-or-restore-an-intel-based-mac-apdebea5be51/mac

Apple Silicon Macs:

https://support.apple.com/guide/apple-configurator-2/revive-or-restore-a-mac-with-apple-silicon-apdd5f3c75ad/mac

Tough to say, if it doesn’t respond as it should, could be a hardware issue as well. However, of course, you also can’t boot from an external drive to do anything to it, I suppose that’s a part of the security though, though it should be responding to the power button, which obviously works as it still starts it up.

I think reviving the firmware should do the trick! Otherwise:

Is there other devices connected to your Mac?

Likewise is it connected via WiFi? Or Ethernet adapter?

If you have a backup, and it actually IS a firmware issue, but can’t get to recovery assistant to erase, I’ve found that erasing via Find My, may just fix that, I’ve found it to be related to the firmware, so if you can’t use Apple Configurator, or “Recovery Assistant”, etc, I may erase using Find My from one of your other devices, once done, click on “Activate Mac” then just reinstall the OS.

Just spitballing what I would do and have done, hope something works and it doesn’t need a repair or something. Point number one: Always keep a backup, or two or three! Cheers. Good luck!

https://support.apple.com/guide/icloud/erase-a-device-mmfc0ef36f/icloud

https://support.apple.com/guide/findmy-mac/erase-a-device-fmmbe7bb71f4/mac

Start up your computer in macOS Recovery

1. Choose Apple menu  > Shut Down.
2. Press and hold the power button on your Mac until you see “Loading startup options.”
3. Click Options, then click Continue. 
4. Enter the password for an administrator account.

Yes, I think it’s telling you it needs to be reset. Is there any error code above the Apple.com/restore? What was the reason for going to recovery mode? Do you have a backup? And are you still able to log into your Mac? Are there any other devices connected to your Mac? This info may help, thanks.

Is it an M1 Mac (i.e. 2020).

If not, hold down cmd-R on restart.