"Provide with a bottom" could also be described as "furnishing a base," "equipping with support," or "affording a foundation." Other potential synonyms include "supplying a footing," "outfitting with stability," and "granting a groundwork." Depending on the context, "providing a base" could also be replaced with phrases like "establishing a starting point," "creating a grounding," or "laying a substructure." Regardless of the specific language used, all of these phrases refer to the act of giving something a stable or secure foundation on which to build and grow.