..Ava9oo..
Perhaps to try single-user mode or command-line may work.
If one exists, try original installer media disc DVD from Apple.
..IF you've no discs, you may be able to use these instructions..
With these, (transitional Mac OS X, PowerPC) and then Intel-Mac
may require careful attempts to make due; since older PPC disc
installers won't work with the later Intel-based Macs.
[Instructions: without the actual disc media, should be OK to gain access.]
This, should work in 'Tiger 10.4, Leopard 10.5, & Snow Leopard 10.6.' - to workaround (&/or) reset Admin:
• How to reset your Mac OS X password without an installer disc | MacYourself (Aug 2009)
https://www.macyourself.com/2009/08/03/how-to-reset-your-mac-os-x-password-without-an-installer-disc/
This second one, seems more limited + fewer choices; maybe to Tiger, or Leopard?
• Reset Mac OSX User Password Without CD disk from command line | Steve Stonebraker [Oct 2010]
https://brakertech.com/reset-mac-os-x-admin-user-password-without-cd-disk/
{..my preference: with previous vintage Macs 'w/o' their original media, appears first..}