Greetings nbs1014,
Welcome to Apple Support Communities. Congrats on the new iPhone 14! The answer to your question, yes. You can manually set up the new iPhone, and sync the photos from the old one using iCloud Photos. Set up your iPhone after selecting step 2 of the Apple Support article: Set up your iPhone or iPad
Use Quick Start or set up manually
If you have another device, you can use it to automatically set up your new device with Quick Start.
If you don't have another device, tap Set Up Manually.
Once you are into the device to get set up, go to Settings > sign in to iCloud if needed, or tap your Apple ID > iCloud, and turn on Photos. You can do this on both devices, and your photos will sync from one to the other. Complete details are found here:
Set up and use iCloud Photos
Let us know if you have any questions.
We hope this helps you.