I have forgotten my iPhone password. How can I restore it without losing data?

No backup = No data recovery, sorry.

See these instructions, keeping in mind that if you don't have a backup all data will be lost on that device (except those that you eventually synced to iCloud):

If your device is running iOS 15.2/iPadOS 15.2 or later, AND if you have created a backup to iCloud, you don't need a computer:--> How to reset your iPhone, iPad, or iPod touch when you forgot your passcode - Apple Support

Shouldn't be this case (iOS/iPadOS earlier than 15.2), you need a computer. If you don't have a computer, borrow one from your friends/relatives/neighbors or ask for help at an Apple Store or Authorized Service Provider, then read these suggestions.

Given that to remove the existing passcode you must connect your device via USB to a computer (a Windows PC running the latest iTunes version, or a Mac, which can run iTunes or Finder, depending on the macOS installed on it), pay attention to the specific gestures that you need to perform while connecting your device to the computer.

These are the instructions to re-gain access to your iPhone/iPad:

If it is an iPhone:--> If you forgot your iPhone passcode - Apple Support

If it is an iPad:--> If you forgot your iPad passcode - Apple Support

Also, take a look at this support video about the same matter (for both iPhone and iPad):

https://www.youtube.com/watch?v=7s8-zLG9ySQ

Regards

Giulio

There is only one way to restore and you will lose all data. See these instructions...

If you forgot your iPhone passcode - Apple Support

This is an important security feature. without the erasure , anyone could pick up your phone, restore it and have total access to your data...