Are there free trials of iCloud storage for new users?

You get 5GB for free to determine if the service works for you. If you want additional storage you will have to pay for it. That is better than a trial, since you never have to cancel the 5GB free storage and you won't automatically be charged for it later.

Not available. You can buy additional storage monthly, no contract.

..just like to add that with phones mostly 64GB or bigger, the free 5GB is intended for calendar, contacts, Notes, small document iCloud Drive etc, not iCloud Photos or iCloud backup .

Another problem with a free trial of, say, 200GB for your iCloud Photos, if you decide not to keep it, after 30 days, pffft your photos disappear forever.