Google announced that you can now make some edits to Google My Business listings as an unverified business owner within Google My Business. Google said "Business owners will be able to suggest edits to some core business information directly from their Google My Business account before verifying their business. This is like the “Suggest an edit” experience, but for unverified business owners."
Google said these edits "will go through the regular review process, and pending review, these changes can go live before verification on Google Search or Maps."
The changes you can make include the name, category, address, hours, phone number, and website. After approval, these changes can be published even before the business is verified on Google Search and Maps. Some users may still need to verify their business first before editing their information.
Forum discussion at Google Help.