Yes, you have to wait just like everyone else.
Any person who hasn’t held H-1 in the past, needs to wait until April 1 to have their H-1 petition filed. If you are already in US, then the petition will be accompanied w/ COS from H-4 to H-1. Once USCIS approves the H-1 petition w/ COS (change of status), you can start working on H-1 from COS effective date (Oct 1 or later).
You can find direct employers as well, but usually consulting companies are more willing to file H-1 for people who are on H-4 (as the company needs to wait for 6 months before you start employment).