How do I connect my Apple TV box to my iPhone without the remote to the Apple TV?

What is your exact model Apple TV? Identify your Apple TV model - Apple Support

For the Apple TV (2nd generation), your option is:

• buy a replacement Apple Remote (aluminum).

The Apple TV (3rd generation) may need a functional remote to set up the Apple TV Remote widget in Control Center on iPhone or iPad.

For the Apple TV (3rd generation), your options are:

• buy a replacement Apple Remote (aluminum);
• temporarily borrow an Apple Remote (aluminum) to help set up the software remote;
• restore the Apple TV and connect a wireless keyboard to help set up the software remote;
• restore the Apple TV and connect the CiderTV Mac app to help set up the software remote.

The Apple TV (4th, 5th, or 6th generation) should recognize the Apple TV Remote widget in Control Center, even without a physical remote, but both have to be one the same network already. I don’t think it will work for setup. The response code typing will be reversed for these models.

Set up the Apple TV Remote on your iPhone, iPad, or iPod touch - Apple Support

You don't need the remote to connect your phone. Go to Control Center. Select remote. You should be able to connect to a device on your network.

Hmmm. I thought it displayed a code on your TV to enter on your device. Sorry about that.

Maybe there is a user group in your area that you could contact.

https://appleusergroupresources.com/find-a-group/