if you pif for the first six months, which is probably a good way to build history anyway, the apr won't matter. after 6 mos., you can then see about a reduction request.
however, if you plan to responsibly carry a balance you could ask sooner. your eq may be a bit low though. come to think of it, i asked for an apr reduction soon after receiving my amex clear (this was before i was a little more credit savvy) card and it was granted... so you never know. you may get lucky with an early request too, i personally wouldn't want to push any lender particularly a new one that i only narrowly qualified for during a recession...but as always YMMV.
I would recommend that you call and request a lower APR. The only thing they will do is say no, or lower the rate.
Bankrate reported that the average cards are now 13.42 Fixed and 11.26 variable.
That 19.99% is pretty high. If they refuse to lower the APR, just use the card and pay in full. Maybe, as others have suggested, wait about six months and try again.