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.
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.