The code requires that a crawl space be provided where a framed floor exists.
That said, some AHJ will allow you to omit the crawlspace if the wood framed floor consists of joists bearing upon PT sleepers that sit on the existing slab-on-grade. They may require that the joist cavity be separated by a vapor barrier, and that no plumbing, mechanical, or electrical be run in the floor.
I suggest that you develop a plan, and then run it past the AHJ.
R408.4 Access
Access shall be provided to all under-floor spaces. Access openings through the floor shall be a minimum of 18 inches by 24 inches (457 mm by 610 mm). Openings through a perimeter wall shall be not less than 16 inches by 24 inches (407 mm by 610 mm). Where any portion of the through-wall access is below grade, an areaway not less than 16 inches by 24 inches (407 mm by 610 mm) shall be provided. The bottom of the areaway shall be below the threshold of the access opening. Through wall access openings shall not be located under a door to the residence. See Section M1305.1.4 for access requirements where mechanical equipment is located under floors.