can a visit to the Apple Store can speed up the account recovery on a stolen iPhone?

This is what Apple says about that:

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.

They don't say if visiting a store would be any faster but it strikes me from the above statement that it wouldn't necessarily, particularly since a store may not be set up to handle security related issues. If you really want to know, ask Apple:

"This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues." --> Contact Apple for help with Apple ID account security - Apple Support

You can set up the new iPhone without an Apple ID and just use it for Safari, texts and phone calls only for the time being. During set up:

1. Choose your preferred language and select your location.
2. Now, two options will be visible. Click on the Set up Manually option to continue.
3. Connect to a Wi-Fi network or use your Cellular data to activate and continue setting up your iPhone.
4. You can now create a passcode, set up Touch ID or Face ID. If you don’t want to use any of these features, click Set up Later in Settings.
5. Now, you will come up with an option to transfer or restore your data from the old iPhone to the new iPhone, but as this is a new setup without using Apple ID, click on the Set Up as New iPhone option.
6. Next, click on Forgot password or Don’t have an Apple ID? Click on Set Up Later in Settings, and a dialog box will pop up asking if you are sure you don’t want to use an Apple ID.
7. Finally, click on Don’t use to confirm, and you will be able to set up iPhone without Apple ID.

Apple cannot help bypass or speed up account recovery. The customer is in full control of their Apple ID from their end only and account recovery is an automated process.