However, what you do need is an "impact rating" calculated by Web of Science(TM). That rating is based on the number of citations articles in your journal gets from other rated journals.
Since your journal is new, it won't have an impact rating, meaning scientists won't publish in it, meaning you won't get an impact rating.
But the alternatives exists, e.g. Bentham and Hindawi are both running spamtastic marketing campaigns for 100s of open access journals, most with none or negligible impact ratings.
There are good and successful ones too. PLoS have very high quality open access journals. Expensive, though.
But again, there are good open access journals out there. And even traditional publishers typically allows open access for individual articles for an additional fee. While these fees may seem high, they will typically only constitute a small fraction of a research grant, so if you care and you plan for it in advance, there is really no excuse for not going open access.