The verb for “to eat” derived from the root √MAT of the same meaning (VT39/7).
Conceptual Development: This verb and root are quite well established, dating all the way back to ᴱQ. mat- and ᴱ√MATA of the Qenya Lexicon of the 1910s (QL/59) and appearing as ᴹQ. mat- and ᴹ√MAT in The Etymologies of the 1930s (Ety/MAT), as well as numerous other places albeit with occasional variants like mata- (PE12/26). This verb was one Tolkien often used in examples of verb conjugations and as such its inflected forms changed considerably over time, but that is more a topic of the evolution of the Quenya verb system itself.
A noun for “food” from the Common Eldarin: Verb Structure (EVS2) of the early 1950s, derived from primitive ✶matnā, originally an ancient adjective meaning “eaten” (PE22/136).
Conceptual Development: In the Qenya Lexicon of the 1910s the word for “food” was ᴱQ. matl under the early root ᴱ√MATA (QL/59). This became ᴱQ. {masta} >> matso in Early Qenya Word-lists of the 1920s (PE16/141). In EVS2 the word was originally manna “food”, but this was struck through and replaced by matta (PE22/136 note #36), which likely reflects Tolkien’s shift in the phonetic developments of primitive tn, so that tn became tt rather than nn as it did in Tolkien’s earlier writings (PE19/85 and note #79).
Neo-Quenya: I find the phonetic developments associated with the above sound change to be problematic for various reasons. Therefore, I prefer to assume the primitive form of this word was an ancient noun: ✱mattā.