The earliest word for “food” in precursors to the Sindarin language was G. môs “food (of men)” (GL/56, 58), probably based on the early root ᴱ√M(B)ASA “cook, bake” (QL/59). This became ᴱN. math “food” in Early Noldorin Word-lists of the 1920s, appearing only in its lenited form vath as an element in ᴱN. orvath “foodless” (PE13/155). In The Etymologies of the 1930s Tolkien had N. mann “food” as a derivative of primitive ᴹ✶matna under the root ᴹ√MAT “eat”, but the version of the entry where this form appeared was struck out (EtyAC/MAT). The primitive form ✶matnā “food” did reappear in the early 1950s, however (PE22/136).
Neo-Sindarin: Of the above, I prefer ᴺS. math for “food”. I first saw math proposed as the Neo-Sindarin word for “food” in a list of neologisms by Elaran on the Vinyë Lambengolmor Discord Server (VLDS) from 2018. I prefer math because I tend to assume Q. matta is derived from ✱mattā rather than ✶matnā to avoid certain phonological difficulties; see that entry for discussion. If you are not concerned with those difficulties, ᴺS. mann “food” is also viable.
A noun for “cooked food, meat” in The Etymologies of the 1930s derived from the root ᴹ√AP, likely from primitive ✱apsā given its Quenya cognate ᴹQ. apsa (Ety/AP). If so, the ae is the result of the vocalization of the ancient ap to ai, after which the diphthong ai became ae.
Neo-Sindarin: This 1930s Noldorin word presents two problems for its adaptation to Sindarin. First, the Sindarin vocalization of ancient p seems to be u rather than i, as in S. leutha- “pick up” < ✱lepta- (VT47/10). Second, it seems spirants no longer vocalized before s, as in S. ach “neck” < aks (PE17/92). Nevertheless, I would retain this word for purposes of Neo-Sindarin and assume it was the result of dialectical variations in Sindarin of the First Age.