How do I reset my forgotten Apple ID password now?

I presume you are indeed in account recovery? You may indeed be able to speed this up. From: How to use account recovery when you can’t reset your Apple ID password - Apple Support

"In some cases, you might be able to speed up the account recovery process or reset your password immediately by verifying a six-digit code sent to your primary email address. You might also be able to shorten the wait time by providing credit-card details to confirm your identity. If you’re given this option, an authorization request goes to the card issuer." - see the document for more details.

Try and reset it at iforgot.apple.com

If you're enrolled in account recovery, the waiting time is what it is and there is no way to speed that up