Just a few days ago, there was a thread about non-Pauline Christianity. I.e. the Council of Jerusalem, or something around that time, basically in the 1st century CE.
While Aramaic certainly was the language of most Jesus-followers among Judaism, their choice of a sacral language would certainly be Hebrew.
By the way, such a much more Jewish Christianity might treat most of what we call the "New Testament" as a rather loose collection of texts with a status more akin to OTL Judaism`s Mishnah and Talmud, and maybe even really overlapping with them. Accounts of the life of Jesus would certainly be considered to be a part of the Tanakh, but that might be it. All the rest (which certainly wouldn`t include Paul´s epistles since only a non-Pauline Christianity can plausibly be expected to favour Hebrew over Greek) would assume a different status and might be in Hebrew, Aramaic or maybe even other languages. It´s difficult to stop that from happening, with a Jewish Christianity, it is only (but firmly so) the Tanakh which can be linguistically strictly controlled. (Especially so if we consider that TTL´s Judaism is, quite generally, going to be more proselytising and less reclusive, given the absence of imperially enforced Christianity.)