There is no way to incorporate in 24 hours. You can buy a shelf company.
Company24H / Companias en 24 Horas - Inicio
You can register a company also via
Cuenta de Usuario
I have started the process via this page. It is VERY EASY. I had to take the process OFF-line because the page works (for now) only with the Santo Domingo Chamber of Commerce, and I am in Higuey. But I had gotten my name registered at ONAPI quick and easy (via creatuempresa.gob.do) now I am dowing the work offline (Registro mercantil and DGII).
The website is operated by Consejo Nacional de Competitividad - very good response. Laura de Castillo and Pamela Salvatore. Can help with many problem on the site and answer questions.
But the whole process takes: about 2 days for ONAPI, 2 days for Registro mercantil, 5 days for DGII (to get RNC#). That is if you have all documents ready (like copies of passports, notarial declarations, statutes, list fo shareholders, etc.) and can just fly by the pages. If you need to "do the work" between the stops it will take more time.
All in all, no way to incorporate in 24 hours.