By "open", I would say you mean "create new project"? If so, yes, you will need an add-on or code to do it, as it normally requires admin permissions.
There are some add-ons that can help you delegate the rights. A simple script is a little more difficult though, as project creation involves creating, copying or reusing a whole set of schemes. I would also be cautious about it, having had the joy of cleaning up more than one JIRA where it's been delegated to users and they have 5,000 junk projects with an average of 3 issues in them.
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