If you have not yet in US by the time your H1 petition was filed, yours is not Change of Status petition.
In this case, you can enter into US with H4 stamped visa at any time. After arriving into US, you need to get your COS filed from H4-H1 (if your H1 was approved ).
The best bet for you is to enter into US with your H4 stamped AFTER filing your H1 papers. Once you arrive into US, try for a job. If you get a job, have your employer file your COS from H4 to H1. Its the SAFEST option for you.