In general, the more you pay your writers, the more submissions you'll get.
For a brand new journal, I would expect that the editor has plenty of ties in the industry and lots of links with authors. (IMO, a journal whose editor has no industry experience and no networks is not an editor who has any business managing a brand new journal.) The editor can contact authors s/he knows and ask them to submit to the journal. Then, once some stories have been contracted, the journal can put in their Calls for Submissions the info that "Issue 1 will include stories by Big Name 1, Household Name 2, and Award Winning Name 3" or whatever, to let potential authors know that authors they admire and respect are publishing in this journal.
There are also usually a number of blogs and websites that do market listings for various genres. Seek them out and get your journal added to them.
Adding: Make sure that the journal's website is proofread and edited, too. Incorrect spelling/punctuation, such as the use of the "grocer's apostrophe", is going to send most authors running.
Finally, respect the privacy of authors. Once a contract has been signed, you can put the author's name on the ToC. But for many authors, the markets they submit to (and get rejected by!) is their own business, not the world's, and they would not be happy to have that information made public.