The Pentateuch established a priesthood for Israel, with very detailed prescriptions for ritual, dress, and functions. According to the author of the Letter to the Hebrews, this was later fulfilled in Christ’s action as Priest:
16. Thus we observe that when God institutes the Old Law, He makes provision besides for sacred rites, and determines in exact detail the rules to be observed by His people in rendering Him the worship He ordains. To this end He established various kinds of sacrifice and designated the ceremonies with which they were to be offered to Him. His enactments on all matters relating to the Ark of the Covenant, the Temple and the holy days are minute and clear. He established a sacerdotal tribe with its high priest, selected and described the vestments with which the sacred ministers were to be clothed, and every function in any way pertaining to divine worship.[Cf. Book of Leviticus] Yet this was nothing more than a faint foreshadowing[Cf. Heb.10:1] of the worship which the High Priest of the New Testament was to render to the Father in heaven.
This isn’t to suggest that Temple worship wasn’t a genuine offering of liturgy to the Father. But it does suggest, however “faintly,” that the celebration of Mass is part of a common heritage.