Good evening afbrn17,
Welcome to the Apple Support Communities!
Congratulations on the purchase of your new iPhone 11. I understand you are trying to transfer data from your previous iPhone to the new one. Are you using Quick Start or are you restoring from a backup?
You may need to cancel the data transfer to address the storage issue. Please make sure you have a backup of your previous iPhone before proceeding.
How to back up your iPhone, iPad, and iPod touch
What is the storage capacity of your previous iPhone compared to your new iPhone?
How to check the storage on your iPhone, iPad, and iPod touch - this will show you what apps or content are taking up space on your iPhone.
You may decide to trade in your new iPhone for a model with storage capacity equal to or greater than your previous iPhone.
Or, on your previous iPhone, you may be able to change some settings to reduce the amount of data being stored on the iPhone. For example, if you don't have iCloud Photos enabled on your previous iPhone, you can enable it and choose the Optimize feature.
Before doing that, check to see how much space you have available in iCloud -
About storage on your device and in iCloud
Manage your photo and video storage
You can also enable iCloud for other features like Contacts, Calendars, Notes, etc. on your previous iPhone. This will also reduce the amount of space taken up on the previous iPhone. On the new iPhone, you will enable these same features.
Change your iCloud feature settings
Once you've made these changes, and backed up your previous iPhone again, you can try to set up your new iPhone again.
Set up your iPhone, iPad, or iPod touch
Take care.