Is it possible to update my iMac without the software update password?

If you cannot remember your password(s) you will have to reset them. They can't be reclaimed. You can use the link below to do so. This time I suggest that you write them down and save them in a safe place for the next time you need them.

Change or reset the password of a macOS user account - Apple Support

There would be potentially two possible passwords when updating macOS:

1. The one used for your Apple ID.
2. The user account on your Mac that has Administrator privileges.

These can both be different ... so, it would help if you can tell us what you were trying to update and provide us a screenshot of the password prompt you are seeing.