If it's the IT managed computer login then you couldn't use a password manager for it, right?
I think this is more the realm of using windows hello or apple touchid (AFAIK no good, simple, standard built-in way exists for linux distros) to get the first OS login and then you can use your password manager when you are logged into the OS.
What method/program are you talking about? Does it support FDE? Is it reasonably supported with the methods expected by end users (fingerprint, face, smartcard, etc.)?
Everytime I've tried its been finicky and had to use non-standard tools to get it working.
I'm a different commenter but yeah, solutions exist. For example systemd-cryptenroll let's you use a FIDO token (or TPM or PKCS#11 smartcard) to unlock your encrypted disk and it's very easy to set up. Quite literally a single command.
Windows Hello serves the same purpose for Windows, though I'm sure there are caveats/differences.
If it's a fido hardware token you still need to make sure you have a backup token. It's a lot simpler on windows/macos where you can use biometrics for the same purpose.
I think this is more the realm of using windows hello or apple touchid (AFAIK no good, simple, standard built-in way exists for linux distros) to get the first OS login and then you can use your password manager when you are logged into the OS.